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Maximal Operators of Vilenkin–Nörlund Means

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Abstract

In this paper we prove and discuss some new \(\left( H_{p},weak-L_{p}\right) \) 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.

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Acknowledgments

We thank the careful referees for some good suggestions, which improved the final version of this paper. The research was supported by Shota Rustaveli National Science Foundation Grant No. 13/06 (Geometry of function spaces, interpolation and embedding theorems. The research was also supported by a Swedish Institute scholarship, provided within the framework of the SI Baltic Sea Region Cooperation/Visby Programme.

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Authors and Affiliations

  1. Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 , Luleå, Sweden

    L.-E. Persson & P. Wall

  2. Narvik University College, P.O. Box 385, 8505, Narvik, Norway

    L.-E. Persson

  3. Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze Str. 1, 0128 , Tbilisi, Georgia

    G. Tephnadze

Authors
  1. L.-E. Persson
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  2. G. Tephnadze
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  3. P. Wall
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Correspondence to L.-E. Persson.

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Communicated by Paul Butzer.

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Persson, LE., Tephnadze, G. & Wall, P. Maximal Operators of Vilenkin–Nörlund Means. J Fourier Anal Appl 21, 76–94 (2015). https://doi.org/10.1007/s00041-014-9345-2

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  • DOI: https://doi.org/10.1007/s00041-014-9345-2

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