Almost everywhere convergence of (C, α)-means of cubical partial sums of d-dimensional Walsh-Fourier series

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37 Citations (Scopus)

Abstract

In the paper we prove that the maximal operator of the fenced(C, α)-means of cubical partial sums of d-dimensional Walsh-Fourier series is of weak type (1,1). Moreover, the fenced(C, α)-means σnα f of the function f ∈ L1 converge a.e. to f as n → ∞.

Original languageEnglish
Pages (from-to)8-28
Number of pages21
JournalJournal of Approximation Theory
Volume141
Issue number1
DOIs
Publication statusPublished - Jul 2006
Externally publishedYes

Keywords

  • Almost everywhere convergence
  • Cesàro means
  • Multiple Walsh-Fourier series

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • General Mathematics
  • Applied Mathematics

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