Cesàro means of double Walsh-Fourier series

Ushangi Goginava

doi:10.1007/s10476-005-0516-x

Cesàro means of double Walsh-Fourier series

Ushangi Goginava

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

6 Citations (Scopus)

Abstract

We investigate approximation properties of Cesàro (C; -α, -β)-means of double Walsh-Fourier series with α, β ∈ (0, 1). As an application, we obtain a sufficient condition for the convergence of the means σ_n,m^/-α,-β (f; x, y) to f(x,y) in the L^p-metric, p ∈ [1, ∞]. We also show that this sufficient condition cannot be improved.

Original language	English
Pages (from-to)	289-304
Number of pages	16
Journal	Analysis Mathematica
Volume	30
Issue number	4
DOIs	https://doi.org/10.1007/s10476-005-0516-x
Publication status	Published - Dec 2004
Externally published	Yes

ASJC Scopus subject areas

Analysis
General Mathematics

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abstract = "We investigate approximation properties of Ces{\`a}ro (C; -α, -β)-means of double Walsh-Fourier series with α, β ∈ (0, 1). As an application, we obtain a sufficient condition for the convergence of the means σn,m/-α,-β (f; x, y) to f(x,y) in the Lp-metric, p ∈ [1, ∞]. We also show that this sufficient condition cannot be improved.",

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AB - We investigate approximation properties of Cesàro (C; -α, -β)-means of double Walsh-Fourier series with α, β ∈ (0, 1). As an application, we obtain a sufficient condition for the convergence of the means σn,m/-α,-β (f; x, y) to f(x,y) in the Lp-metric, p ∈ [1, ∞]. We also show that this sufficient condition cannot be improved.

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Cesàro means of double Walsh-Fourier series

Abstract

ASJC Scopus subject areas

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