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

Ushangi Goginava

doi:10.1016/j.jat.2006.01.001

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

Ushangi Goginava

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

39 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 σ_n^α f of the function f ∈ L¹ converge a.e. to f as n → ∞.

Original language	English
Pages (from-to)	8-28
Number of pages	21
Journal	Journal of Approximation Theory
Volume	141
Issue number	1
DOIs	https://doi.org/10.1016/j.jat.2006.01.001
Publication status	Published - Jul 2006
Externally published	Yes

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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10.1016/j.jat.2006.01.001

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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 → ∞.",

keywords = "Almost everywhere convergence, Ces{\`a}ro means, Multiple Walsh-Fourier series",

author = "Ushangi Goginava",

year = "2006",

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AB - 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 → ∞.

KW - Almost everywhere convergence

KW - Cesàro means

KW - Multiple Walsh-Fourier series

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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