Almost everywhere strong summability of double Walsh-Fourier series

G. Gát; U. Goginava

doi:10.3103/S106836231501001X

Almost everywhere strong summability of double Walsh-Fourier series

G. Gát
, U. Goginava

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

1 Citation (Scopus)

Abstract

In this paper we study a question of almost everywhere strong convergence of the quadratic partial sums of two-dimensional Walsh-Fourier series. Specifically, we prove that the asymptotic relation (Formula presented.) holds a.e. for every function of two variables belonging to L logL and for 0 < p ≤ 2. Then using a theorem by Getsadze [6] we infer that the space L log L can not be enlarged by preserving this strong summability property.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Journal of Contemporary Mathematical Analysis
Volume	50
Issue number	1
DOIs	https://doi.org/10.3103/S106836231501001X
Publication status	Published - Jan 1 2015
Externally published	Yes

Keywords

a. e. convergence
strong Marcinkiewicz means
Two-dimensional Walsh system

ASJC Scopus subject areas

Analysis
Control and Optimization
Applied Mathematics

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10.3103/S106836231501001X

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abstract = "In this paper we study a question of almost everywhere strong convergence of the quadratic partial sums of two-dimensional Walsh-Fourier series. Specifically, we prove that the asymptotic relation (Formula presented.) holds a.e. for every function of two variables belonging to L logL and for 0 < p ≤ 2. Then using a theorem by Getsadze [6] we infer that the space L log L can not be enlarged by preserving this strong summability property.",

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N2 - In this paper we study a question of almost everywhere strong convergence of the quadratic partial sums of two-dimensional Walsh-Fourier series. Specifically, we prove that the asymptotic relation (Formula presented.) holds a.e. for every function of two variables belonging to L logL and for 0 < p ≤ 2. Then using a theorem by Getsadze [6] we infer that the space L log L can not be enlarged by preserving this strong summability property.

AB - In this paper we study a question of almost everywhere strong convergence of the quadratic partial sums of two-dimensional Walsh-Fourier series. Specifically, we prove that the asymptotic relation (Formula presented.) holds a.e. for every function of two variables belonging to L logL and for 0 < p ≤ 2. Then using a theorem by Getsadze [6] we infer that the space L log L can not be enlarged by preserving this strong summability property.

KW - a. e. convergence

KW - strong Marcinkiewicz means

KW - Two-dimensional Walsh system

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Almost everywhere strong summability of double Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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