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

Ushangi Goginava; Giorgi Oniani

doi:10.5486/PMD.2020.8680

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

Ushangi Goginava
, Giorgi Oniani

Research output: Contribution to journal › Article › peer-review

2 Citations (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,...,φ_dconverge almost everywhere, then the product system φ₁× · · ·×φ_dalso has a similar property for a quite general type of partial sums.

Original language	English
Pages (from-to)	313-320
Number of pages	8
Journal	Publicationes Mathematicae Debrecen
Volume	97
Issue number	4
DOIs	https://doi.org/10.5486/PMD.2020.8680
Publication status	Published - 2020

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.5486/PMD.2020.8680

Cite this

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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{\texttimes} · · ·{\texttimes}φdalso has a similar property for a quite general type of partial sums.",

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AU - Oniani, Giorgi

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AB - 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.

KW - Almost everywhere convergence

KW - Lacunary partial sums

KW - Multiple Fourier series

KW - Square summable function

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

Abstract

Keywords

ASJC Scopus subject areas

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