On the almost everywhere convergence of multiple Fourier series of square summable functions

Ushangi Goginava, Giorgi Oniani

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We prove that if the lacunary partial sums of the Fourier series of every square summable function concerning each one-dimensional orthonormal system φ1,...,φdconverge almost everywhere, then the product system φ1× · · ·×φdalso has a similar property for a quite general type of partial sums.

Original languageEnglish
Pages (from-to)313-320
Number of pages8
JournalPublicationes Mathematicae Debrecen
Volume97
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Almost everywhere convergence
  • Lacunary partial sums
  • Multiple Fourier series
  • Square summable function

ASJC Scopus subject areas

  • General Mathematics

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