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• 1.
Stockholm University, Faculty of Science, Department of Mathematics.
A variant of Yano's extrapolation theorem on Hardy spaces2019In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 113, no 5, p. 537-549Article in journal (Refereed)

In this note, a variant of Yano's classical extrapolation theorem for sublinear operators acting on analytic Hardy spaces over the torus is obtained.

• 2. Boyvalenkov, Peter
Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Data Transmission.
Uniqueness of the 120-point spherical 11-design in four dimensions2001In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 77, no 4, p. 360-368Article in journal (Refereed)

We prove that on the Euclidean sphere S-3 there exist a unique up to isometry 120-point spherical 11-design and a maximal (4, 120, cos(pi /5)) -code. Both these are nothing but copies of a famous regular polytope in four dimensions-the 600-cell.

• 3.
Department of Mathematics, Central University of Venezuela.
Faculty of Mathematics and Computer Science, Adam Mickiewicz University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Orlicz spaces which are AM-spaces1997In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 69, no 3, p. 234-242Article in journal (Refereed)

The Orlicz function and sequence spaces which are AM-spaces are characterized for both the Luxemburg-Nakano and the Amemiya (Orlicz) norm.

• 4.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Minimality and (weighted) interpolation in Paley-Wiener spaces2014In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 102, no 4, p. 379-389Article in journal (Refereed)

We investigate links between minimality, Carleson condition, and (weighted) interpolation in Paley-Wiener spaces. In particular, we show that the Carleson condition on a sequence. together with minimality in Paley-Wiener spaces PW iota p implies the interpolation property of Lambda in PW iota+epsilon p, for every epsilon > 0. This result does not, surprisingly, require uniform minimality.

• 5.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Nonbranching weak and starshaped strong solutions for Hele-Shaw dynamics2005In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 84, no 6, p. 551-558Article in journal (Refereed)

We consider multidimensional weak and strong Hele-Shaw dynamics Omega(t) of an advancing/receding viscous fluid injected/removed through a single finite point into/from a bounded domain Omega(0). A class of weak solutions is shown to preserve local uniqueness in both directions. Then we also consider strong solutions Omega(t), and show that if Omega(0) is starshaped with respect to a small ball centered on the point of injection, then the evolution Omega(t) exists for all time.

• 6.
KTH, Superseded Departments, Mathematics.
Formal power series and nearly analytic functions1991In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 57, p. 61-70Article in journal (Refereed)
• 7.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On g-functions for countable state subshifts2017In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 109, no 4, p. 373-381Article in journal (Refereed)

This note revisits the problem of finding necessary and sufficient conditions for a subshift to admit a continuous g-function. Results obtained by Krieger (in: IMS lecture notes monograph series, vol 48, pp 306-316, 2006) on finite alphabet subshifts are generalized to countable state subshifts.

• 8. Kawohl, B.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Gamma limits in some Bernoulli free boundary problem2005In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 84, no 1, p. 79-87Article in journal (Refereed)

We study the limit cases p --> infinity and p --> 1 of the functionals (1) E-p(u) := integral(Rn) {1/p(|delu|/a) (p) + p-1/ p chi({u>0})} dx, where u = 1 on a given compact set K subset of R-n, and a > 0 is also given. Minimizers u(p) of these functionals have uniformly bounded support Omega(p) := {u(p) > 0} and satisfy (2) - Delta(p)u(p) = 0 in Omega(p), u(p) = 1 on K, |delu(p)| = a on partial derivativeOmega(p).

• 9. Maligranda, Lech
A property of interpolation spaces1987In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 48, no 1, p. 82-84Article in journal (Refereed)
• 10.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Positive bilinear operators in Calderón-Lozanovskii spaces2003In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 81, no 1, p. 26-37Article in journal (Refereed)

A generalization of an abstract Hölder-Rogers inequality for positive bilinear operators is proved. Then it is used in the theory of interpolation of operators. An interpolation theorem for positive bilinear operators between Calderón-Lozanovskii spaces holds if and only if the parameter functions generating those spaces satisfy a generalized C-supermultiplicativity condition (2). In the case when all generating functions are the same this condition is exactly the same as the C-supermultiplicativity condition on the function.

• 11.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematics, Osaka Kyoiku University.
Pointwise multipliers of Orlicz spaces2010In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 95, no 3, p. 251-256Article in journal (Refereed)

We show that the result on multipliers of Orlicz spaces holds in general. Namely, under the assumption that three Young functions Φ1, Φ2 and Φ, generating corresponding Orlicz spaces, satisfy the estimate for all u > 0, we prove that if the pointwise product xy belongs to L Φ(μ) for all , then . The result with some restrictions either on Young functions or on the measure μ was proved by Maligranda and Persson (Indag. Math. 51 (1989), 323-338). Our result holds for any collection of three Young functions satisfying the above estimate and for an arbitrary complete σ-finite measure μ.

• 12. Maligranda, Lech
Department of Mathematics, Central University of Venezuela.
Interpolation of weakly compact operators1990In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 55, no 3, p. 280-284Article in journal (Refereed)
• 13.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
Categorification of Wedderburn's basis for C[S-n]2008In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 91, no 1, p. 1-11Article in journal (Refereed)

M. Neunhoffer studies in [21] a certain basis of C[S-n] with the origins in [14] and shows that this basis is in fact Wedderburn's basis, hence decomposes the right regular representation of S-n into a direct sum of irreducible representations (i.e. Specht or cell modules). In the present paper we rediscover essentially the same basis with a categorical origin coming from projective-injective modules in certain subcategories of the BGG-category O. Inside each of these categories, there is a dominant projective module which plays a crucial role in our arguments and will additionally be used to show that Kostant's problem ([10]) has a negative answer for some simple highest weight module over the Lie algebra sl(4). This disproves the general belief that Kostant's problem should have a positive answer for all simple highest weight modules in type A.

• 14.
Department of Mathematics, Sofia University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, University of Athens, Panepistimiopolis.
On Clarkson's inequality, type and cotype for the Edmunds-Triebel logarithmic spaces2003In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 80, no 2, p. 165-176Article in journal (Refereed)

We show that the (p, p') Clarkson's inequality holds in the Edmunds-Triebel logarithmic spaces Aq(logA)b,q and in the Zygmund spaces Lp(logL)b(W), for b Î \mathbbR and for suitable 1 £ p £ 2. As a consequence of these results we also obtain some new information about the types and the cotypes of these spaces.

• 15. Skrzypczak, Leszek
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
A geometric criterion for compactness of invariant subspaces2013In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 101, no 3, p. 259-268Article in journal (Refereed)

Let M be a non-compact homogeneous Riemannian manifold, and let Omega be a compact subgroup of isometries of M. We show, under general conditions, that the Omega-invariant subspace A (Omega) of a normed vector space is compactly embedded into L (q) (M) if and only if the group Omega has no orbits with a uniformly bounded diameter in a neighborhood of infinity.

• 16.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
A note on the differentiability of conjugate functions2009In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 93, no 5, p. 481-485Article in journal (Refereed)

For a proper, lower semicontinuous and convex function f with Legendre-Fenchel conjugate f *, it is well-known that differentiability properties of f * are equivalent to strict convexity properties of f. In this note a result of this kind is obtained without a convexity assumption on f.

• 17.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Hamilton-Jacobi equations having only action functions as solutions2004In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 83, no 5, p. 437-449Article in journal (Refereed)

Let L(x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H(x, p) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution ....

• 18.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On viscosity solutions of irregular Hamilton-Jacobi equations2003In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 81, no 6, p. 678-688Article in journal (Refereed)

In this paper, the author proves the existence and uniqueness of continuous viscosity solutions for some Hamilton-Jacobi equations with possibly discontinuous Hamiltonians. As a corollary, he gets the existence and uniqueness of continuous viscosity solutions for some transport equations with discontinuous coefficients.

• 19.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Semiconcavity estimates for viscous Hamilton-Jacobi equations2010In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 94, no 6, p. 579-589Article in journal (Refereed)

We present sharp Hessian estimates of the form {Mathematical expression} for the solution of the viscous Hamilton-Jacobi equation {Mathematical expression}The smallest possible positive function g(t) is explicitly given in terms of the semiconvexity and semiconcavity parameters of V and S0, respectively. The optimal g does not depend on the viscosity parameter {Mathematical expression} . The potential V and the initial function S0 are allowed to grow quadratically

• 20.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
On the Blocki-Zwonek conjectures and beyond2015In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 105, no 4, p. 371-380Article in journal (Refereed)

Let $${\Omega}$$ be a bounded pseudoconvex domain in $${\mathbb{C}^n}$$, and let $${g_{\Omega}(z,a)}$$ be the pluricomplex Green function with pole at a in $${\Omega}$$. Błocki and Zwonek conjectured that the function given by $$\begin{array}{ll}\alpha = \alpha_{\Omega}, a: (- \infty, 0) \ni t \mapsto \alpha (t) = e^{-2nt} \lambda_n \left( \{z \in \Omega: g_{\Omega}(z, a) < t \} \right)\end{array}$$ is nondecreasing, and that the function given by $$\begin{array}{ll}\beta = \beta_{\Omega}, a: (-\infty, 0) \ni t \to \beta(t)= \log \left(\lambda_n \left(\{z \in \Omega: g_{\Omega}(z,a)< t\}\right)\right)\end{array}$$ is convex. Here $${\lambda_{n}}$$ is the Lebesgue measure in $${\mathbb{C}^n}$$. In this note we give an affirmative answer to these conjectures when $${\Omega}$$ is biholomorphic to a bounded, balanced, and pseudoconvex domain in $${\mathbb{C}^n}$$, $${n\geq 1}$$. The aim of this note is to consider generalizations of the functions $${\alpha}$$, $${\beta}$$ defined by the Green function with two poles in $${\mathbb{D}\subset\mathbb{C}}$$. We prove that $${\alpha}$$ is not nondecreasing, and $${\beta}$$ is not convex. By using the product property for pluricomplex Green functions, we then generalize this to n-dimensions. Finally, we end this note by considering two other possibilities generalizing the Błocki–Zwonek conjectures.

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