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351.

Persson, Lars-Erik

et al.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Tephnadze, George

Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University.

Wall, Peter

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Maximal Operators of Vilenkin–Nörlund Means2015In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 2, no 1, p. 76-94Article in journal (Refereed)

Abstract [en]

In this paper we prove and discuss some new (H p ,weak−L p ) type inequalities of maximal operators of Vilenkin–Nörlund means with monotone coefficients. We also apply these results to prove a.e. convergence of such Vilenkin–Nörlund means. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh-Fourier series. We also show that these conditions are in a sense necessary and suffcient.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. RUDN University, Moscow, Russia; UiT The Arctic University of Norway.

Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. School of Informatics, Engineering and Mathematics, The University of Georgia.

Wall, Peter

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Two-sided Hardy-type inequalities for monotone functions are extended. The cases of positive and negative parameter values are also studied. The discrete result of theorem is extended to an arbitrary positive σ-finite Borel measure. The notation A ≪ B means that A≤ cB, where c is a constant depending only on the summation parameter. Different theorems proposed prove the new characterization of the discrete Hardy inequality.

Centre for Mathematical Sciences, Lund University.

Persson, Lars-ErikLuleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.Silvestrov, Sergei D.Division of Applied Mathematics, Mälardalen University.