Almost everywhere convergence of a subsequence of the logarithmic means of quadratical partial sums of double Walsh-Fourier series

György Gát, Ushangi Goginava

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The main aim of this paper is to prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Fourier series is of weak type (1,1) provided that the supremum in the maximal operator is taken over special indicies. The set of Walsh polynomials is dense in L1 (I × I), so by the well-known density argument we have that t2n (x1, 2) → f (x1, x2) a.e. for all integrable two-variable functions f.

Original languageEnglish
Pages (from-to)173-184
Number of pages12
JournalPublicationes Mathematicae Debrecen
Volume71
Issue number1-2
Publication statusPublished - 2007
Externally publishedYes

Keywords

  • a.e. Convergence
  • Double Walsh-Fourier series
  • Logarithmic means

ASJC Scopus subject areas

  • General Mathematics

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