Weak inequalities for Cesàro and Riesz summability of Walsh-Fourier series

Péter Simon, Ferenc Weisz

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The maximal operators for Cesàro or (C, α) and Riesz summability with respect to Walsh-Fourier series are investigated as mappings between dyadic Hardy and Lebesgue spaces. It is well known that they are bounded from Hp to Lp for all 1 / (α + 1) < p < ∞. In this work we prove that this boundedness result does not hold anymore if p ≤ 1 / (α + 1). However, for p = 1 / (α + 1) the maximal operators are bounded from H1 / (α + 1) to the weak L1 / (α + 1) space. To the proof some known estimations for the Cesàro and Riesz kernels have to be sharpened.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalJournal of Approximation Theory
Volume151
Issue number1
DOIs
Publication statusPublished - Mar 1 2008

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Keywords

  • Cesàro and Riesz summability
  • Dyadic Hardy spaces
  • Walsh functions
  • p-Atom

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

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