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• 1.
L.N. Gumilyov Eurasian National University.
L.N. Gumilyov Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 12011In: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 61, no 1, p. 7-26Article in journal (Refereed)

We consider a new Sobolev type function space called the space with multiweighted derivatives W-p(n),(alpha) over bar, where (alpha) over bar = (alpha(0), alpha(1), ......, alpha(n)), alpha(i) is an element of R, i = 0, 1,......,n, and parallel to f parallel to W-p(n),((alpha) over bar) = parallel to D((alpha) over bar)(n)f parallel to(p) + Sigma(n-1) (i=0) vertical bar D((alpha) over bar)(i)f(1)vertical bar, D((alpha) over bar)(0)f(t) = t(alpha 0) f(t), d((alpha) over bar)(i)f(t) = t(alpha i) d/dt D-(alpha) over bar(i-1) f(t), i = 1, 2, ....., n. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W-p,(alpha) over bar(n) -> W-q,(beta) over bar,(m) when 1 <= q < p < infinity, 0 <= m < n

• 2.
L.N. Gumilyov Eurasian National University.
L.N. Gumilyov Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q2009Report (Other academic)
• 3.
University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Tromsø ; The Arctic University of Norway, Narvik.
Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017In: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, no 5-6, p. 599-609Article in journal (Refereed)

Abstract—Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

• 4.
Department of Mathematics, University of Haifa, Haifa, Israel.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UIT The Arctic University of Norway, Narvik, Norway.
Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities2018In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, no 3, p. 759-772Article in journal (Refereed)

In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .

• 5.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 32014In: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 / [ed] Manuel Cepedello Boiso; Håkan Hedenmalm; Marinus A. Kaashoek; Alfonso Montes Rodríguez; Sergei Treil, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2014, p. 1-10Conference paper (Refereed)

For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest

• 6.
Department of Mathematics, University of Haifa.
Faculty of Textile Technology, University of Zagreb. Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new refined Hardy type inequalities with general kernels and measures2010In: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 79, no 1-2, p. 157-172Article in journal (Refereed)

We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator Ak defined by, where k: Ω1 × Ω2 is a general nonnegative kernel, (Ω1, μ1) and (Ω2, μ2) are measure spaces and,. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.

• 7.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Inequalities for averages of quasiconvex and superquadratic functions2016In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, no 2, p. 535-550Article in journal (Refereed)

For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.

• 8.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new estimates of the ‘Jensen gap’2016In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, article id 39Article in journal (Refereed)

Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.

• 9.
University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new scales of refined Hardy type inequalities via functions related to superquadracity2013In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, no 3, p. 679-695Article in journal (Refereed)

For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved

• 10.
University of Haifa, Department of Mathematics.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Zagreb. University of Zagreb.
General inequalities via isotonic subadditive functionals2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 1, p. 15-28Article in journal (Refereed)

In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

• 11.
University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On some new developments of Hardy-type inequalities2012In: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2012, p. 739-746Conference paper (Refereed)

In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.

• 12.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities2015In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, no 2, p. 615-627Article in journal (Refereed)

In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.

• 13.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new scales of refined Jensen and Hardy type inequalities2014In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, no 3, p. 1105-1114Article in journal (Refereed)

Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.

• 14.
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Boundedness and compactness of a class of Hardy type operators2016In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 1, article id 324Article in journal (Refereed)

We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.

• 15.
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, Tromso, Norway. RUDN University, Moscow, Russia.
Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, no 1, p. 201-215, article id 21-16Article in journal (Refereed)

We establish criteria for both boundedness and compactness for some classes of integraloperators with logarithmic singularities in weighted Lebesgue spaces for cases 1 < p 6 q <¥ and 1 < q < p < ¥. As corollaries some corresponding new Hardy inequalities are pointedout.1

• 16.
L. N.Gumilev Eurasian National University, Khazakstan.
L. N.Gumilev Eurasian National University, Khazakstan. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, no 3, p. 683-694Article in journal (Refereed)

Abstract. Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On a new class of Hardy-type inequalities2012In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, no 259Article in journal (Refereed)

In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy's, Hardy-Hilbert's, Hardy-Littlewood-P\'{o}lya's and P\'{o}lya-Knopp's inequalities as well as of Godunova's and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.

• 18.
Department of Pure Mathematics, Eurasian National University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, Narvik University College. Department of Pure Mathematics, Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new results concerning a class of third-order differential equations2015In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, no 2, p. 419-434Article in journal (Refereed)

We consider the following third-order differential equation with unbounded coefficients:Some new existence and uniqueness results are proved, and precise estimates of the norms of the solutions are given. The obtained results may be regarded as a unification and extension of all other results of this type

• 19.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Homogenization of the Reynolds equation2005Report (Other academic)
• 20.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Homogenization of the unstationary incompressible Reynolds equation2007In: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, no 9, p. 1344-1350Article in journal (Refereed)

This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.

• 21.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Homogenization of Reynolds equation2005Report (Other academic)
• 22.
Luleå tekniska universitet.
Luleå tekniska universitet. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå tekniska universitet.
Linjär algebra med geometri1990 (ed. 2)Book (Other (popular science, discussion, etc.))
• 23.
Luleå tekniska universitet.
Luleå tekniska universitet. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå tekniska universitet.
Linjär algebra med geometri1986Book (Other (popular science, discussion, etc.))
• 24.
Luleå tekniska universitet.
Luleå tekniska universitet. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå tekniska universitet. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Linjär algebra med geometri1999Book (Other (popular science, discussion, etc.))
• 25.
Department of Fundamental and Applied Mathematics, Eurasian National University, Munaitpasov str. 4, Astana.
Department of Fundamental and Applied Mathematics, Eurasian National University, Munaitpasov str. 4, Astana. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some New Hardy-type Integral Inequalities on Cones of Monotone Functions2013In: Advances in Harmonic Analysis and Operator Theory: The Stefan Samko Anniversary Volume, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2013, p. 77-89Chapter in book (Refereed)

Some new Hardy-type inequalities with Hardy-Volterra integral operators on the cones of monotone functions are obtained. The case 1 < p ≤ q < ∞ is considered and the involved kernels satisfy conditions which are less restrictive than the classical Oinarov condition.

• 26.
Luleå University of Technology, Department of Engineering Sciences and Mathematics.
L.N. Gumilyov Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On the boundedness of some classes of integral operators in Lebesgue spaces2011Report (Other academic)
• 27.
Luleå University of Technology, Department of Engineering Sciences and Mathematics.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On the boundedness of some classes of integral operators in weighted Lebesgue spaces2012In: Eurasian Mathematical Journal, ISSN 2077-9879, Vol. 3, no 1, p. 5-17Article in journal (Refereed)
• 28.
Luleå University of Technology, Department of Engineering Sciences and Mathematics.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new inequalities on cones of monotone functions2011Report (Other academic)
• 29. Asekritova, Irina
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Lions-Peetre reiteration formulas for triples and their applications2001In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 145, no 3, p. 219-254Article in journal (Refereed)

Two reiteration theorems for triples of quasi-Banach function lattices are given. As a by-product of these, some interpolation results are obtained for block-Lorentz spaces and triples of weighted $L_p$-spaces.

• 30.
Yaroslavl Pedagogical Institute.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Distribution and rearrangement estimates of the maximal function and interpolation1997In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 124, no 2, p. 107-132Article in journal (Refereed)
• 31.
Department of Mathematics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Sharp Hp- Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications2016In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 1, article id 242Article in journal (Refereed)

We prove and discuss some new Hp-Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out

• 32.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Best constants between equivalent norms in Lorentz sequence spaces2012In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 2012Article in journal (Refereed)

We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.

• 33.
Luleå tekniska universitet.
School of Mathematics, University College Cardiff. Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Sharp multidimensional multiplicative inequalities for weighted Lp spaces with homogeneous weights1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 1, p. 53-67Article in journal (Refereed)
• 34.
Luleå tekniska universitet.
Department of Mathematics and Statistics, McMaster University, Hamilton. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Duality theorem over the cone of monotone functions and sequences in higher dimensions2002In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 7, no 1, p. 79-108Article in journal (Refereed)

Let f be a non-negative function defined on ℝ+n which is monotone in each variable separately. If 1 < p < ∞, g ≥ 0 and v a product weight function, then equivalent expressions for sup ∫ℝ(+)(n) fg/(ℝ+nfpv)1/p are given, where the supremum is taken over all such functions f. Variants of such duality results involving sequences are also given. Applications involving weight characterizations for which operators defined on such functions (sequences) are bounded in weighted Lebesgue (sequence) spaces are also pointed out.

• 35.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
A Sawyer duality principle for radially monotone functions in Rn2005In: Journal of Inequalities in Pure and Applied Mathematics, ISSN 1443-5756, E-ISSN 1443-5756, Vol. 6, no 2, article id 44Article in journal (Refereed)

Let f be a non-negative function on ℝn, which is radially monotone (0 < f↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup ∫ℝ fg/f↓r(∫ℝn fp v)1/p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given. © 2005 Victoria University

• 36.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Department of Mathematical Sciences, University of Memphis. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Applied Mathematics and Analysis, University of Barcelona.
Mixed norm and multidimensional Lorentz spaces2005Report (Other academic)
• 37.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Department of Mathematical Sciences, University of Memphis. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Applied Mathematics and Analysis, University of Barcelona.
Mixed norm and multidimensional Lorentz spaces2006In: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 10, no 3, p. 539-554Article in journal (Refereed)

In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces.

• 38.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Optimal estimates between equivalent norms in Lorentz sequence spaces2009Report (Other academic)
• 39.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Technical University of Civil Engineering Bucharest, Department of Mathematics & Computer Science. Technical University of Civil Engineering Bucharest, Department of Mathematics & Computer Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Optimal estimates in Lorentz spaces of swquences with an increasing weight2013In: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 14, no 1, p. 20-27Article in journal (Refereed)
• 40.
Luleå tekniska universitet.
Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Carlson type inequalities1998In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2, no 2, p. 121-135Article in journal (Refereed)

A scale of Carlson type inequalities are proved and the best constants are found. Some multidimensional versions of these inequalities are also proved and it is pointed out that also a well-known inequality by Beurling-Kjellberg is included as an endpoint case.

• 41.
Luleå tekniska universitet.
Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Reversed Hölder type inequalities for monotone functions of several variables1997In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 186, no 67-80, p. 67-80Article in journal (Refereed)
• 42.
Luleå tekniska universitet.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Weighted multidimensional inequalities for monotone functions1999In: Mathematica Bohemica, ISSN 0862-7959, Vol. 124, no 2-3, p. 329-335Article in journal (Refereed)

We discuss the characterization of the inequality  \biggl(\int_{{\Bbb R}^N_+} f^q u\biggr)^{1/q} \leq C \biggl(\int_{{\Bbb R}^N_+} f^p v \biggr)^{1/p},\quad0

• 43.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Lucian Blaga University of Sibiu.
Some multiplicative inequalities for inner products and of the Carlson type2008In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242XArticle in journal (Refereed)

We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.

• 44.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Institute of Mathematics of Romanian Academy.
A matriceal analogue of Fejer's theory2003In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 260, no 1, p. 14-20Article in journal (Refereed)

J. Arazy [1] pointed out that there is a similarity between functions defined on the torus and infinite matrices. In this paper we discuss and develop in the framework of matrices Fejer's theory for Fourier series.

• 45. Barza, Sorina
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On weighted multidimensional integral inequalities for mixed monotone functions2000In: Societe des Sciences Mathematiques de Roumanie. Bulletin Mathematique, ISSN 1220-3874, Vol. 43(91), no 1, p. 39-45Article in journal (Refereed)
• 46.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new sharp limit Hardy-type inequalities via convexity2014In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2014, article id 6Article in journal (Refereed)

Some new limit cases of Hardy-type inequalities are proved, discussed and compared. In particular, some new refinements of Bennett's inequalities are proved. Each of these refined inequalities contain two constants, and both constants are in fact sharp. The technique in the proofs is new and based on some convexity arguments of independent interest.

• 47.
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Applied Mathematics and Analysis, University of Barcelona.
Multidimensional rearrangement and Lorentz spaces2004In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 104, no 3, p. 203-224Article in journal (Refereed)

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.

• 48.
Luleå tekniska universitet.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Departamento de Matemàtica, Aplicada i Anàlisi, Universitat de Barcelona.
Sharp weighted multidimensional integral inequalities of Chebyshev type1999In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 236, no 2, p. 243-253Article in journal (Refereed)

We prove a general Chebyshev inequality for monotone functions in higher dimensions. This result generalizes the classical one-dimensional inequality and recovers some extensions already known for product weights. In all cases we find the best constant in the inequality. We also consider the case of more general operators.

• 49. Barza, Sorina
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Computing Centre, Russian Academy of Sciences, Far-Eastern Branch, Khabarovsk.
On weighted multidimensional embeddings for monotone functions2001In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 88, no 2, p. 303-319Article in journal (Refereed)

We characterize the inequality (∫RN+ fqu)1/q ≤ C(∫RN+fpv)1/p, 0 < q, p < ∞, for monotone functions f ≥ 0 and nonnegative weights u and v. The case q < p is new and the case 0 < p ≤ q < ∞ is extended to a modular inequality with N-functions. A remarkable fact concerning the calculation of C is pointed out

• 50.
Eurasian National University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. The Artic University of Norway. Eurasian National University. Eurasian National University.
Some new hardy-type inequalities in q-analysis2016In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 10, no 3, p. 761-781Article in journal (Refereed)

We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q-analogs of (r, p)-weighted Hardy-type inequalities for all possible positive values of the parameters r and p. We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction

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