On The Convergence And Summability of N-Dimensional Fourier Series with Respect to the Walsh-Paley Systems in the Spaces Lp([0, 1]N), p ∈[1, +∞]

U. Goginava

doi:10.1515/GMJ.2000.53

On The Convergence And Summability of N-Dimensional Fourier Series with Respect to the Walsh-Paley Systems in the Spaces L^p([0, 1]^N), p ∈[1, +∞]

U. Goginava

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

10 Citations (Scopus)

Abstract

The convergence and summability of N-dimensional Walsh-Fou-rier series in the metrics L^p([0, 1]^N), p ∈ [1, +∞], are studied by the negative order Césaro method. Getsadze's theorem and a generalization of Moricz' theorem are obtained as special cases.

Original language	English
Pages (from-to)	53-72
Number of pages	20
Journal	Georgian Mathematical Journal
Volume	7
Issue number	1
DOIs	https://doi.org/10.1515/GMJ.2000.53
Publication status	Published - 2000
Externally published	Yes

Keywords

Césaro summability
Modulus of variation
Multiple Fourier-Walsh series
Uniform convergence

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1515/GMJ.2000.53

Cite this

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abstract = "The convergence and summability of N-dimensional Walsh-Fou-rier series in the metrics Lp([0, 1]N), p ∈ [1, +∞], are studied by the negative order C{\'e}saro method. Getsadze's theorem and a generalization of Moricz' theorem are obtained as special cases.",

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AB - The convergence and summability of N-dimensional Walsh-Fou-rier series in the metrics Lp([0, 1]N), p ∈ [1, +∞], are studied by the negative order Césaro method. Getsadze's theorem and a generalization of Moricz' theorem are obtained as special cases.

KW - Césaro summability

KW - Modulus of variation

KW - Multiple Fourier-Walsh series

KW - Uniform convergence

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