Triangular Cesàro summability of two dimensional Fourier series

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Abstract

It is proved that the maximal operator of the triangular Cesàro means of a two-dimensional Fourier series is bounded from the periodic Hardy space Hp(T2) to Lp(T2) for all 2/(2+α)≤p≦∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular Cesàro means of a function f ∈ L1(T2) converge a. e. to f.

Original languageEnglish
Pages (from-to)27-41
Number of pages15
JournalActa Mathematica Hungarica
Volume132
Issue number1-2
DOIs
Publication statusPublished - Jul 1 2011

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Keywords

  • Cesàro summability
  • Fourier series
  • Hardy space
  • interpolation
  • p-atom
  • triangular summation

ASJC Scopus subject areas

  • Mathematics(all)

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