Almost everywhere summability of multiple Walsh-Fourier series

Ushangi Goginava

doi:10.1016/S0022-247X(03)00503-1

Almost everywhere summability of multiple Walsh-Fourier series

Ushangi Goginava

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

16 Citations (Scopus)

Abstract

We prove that for the N-dimensional Walsh-Fourier series the maximal operator of the Marcinkiewicz means is of weak type (1, 1). Moreover, the Marcinkiewicz means σ_n f of the function f ∈ L¹ converge a.e. to f as n → ∞.

Original language	English
Pages (from-to)	90-100
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	287
Issue number	1
DOIs	https://doi.org/10.1016/S0022-247X(03)00503-1
Publication status	Published - Nov 1 2003
Externally published	Yes

Keywords

Marcinkiewicz means
Multiple Walsh-Fourier series
Summability almost everywhere

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/S0022-247X(03)00503-1

Cite this

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title = "Almost everywhere summability of multiple Walsh-Fourier series",

abstract = "We prove that for the N-dimensional Walsh-Fourier series the maximal operator of the Marcinkiewicz means is of weak type (1, 1). Moreover, the Marcinkiewicz means σn f of the function f ∈ L1 converge a.e. to f as n → ∞.",

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author = "Ushangi Goginava",

year = "2003",

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T1 - Almost everywhere summability of multiple Walsh-Fourier series

AU - Goginava, Ushangi

PY - 2003/11/1

Y1 - 2003/11/1

N2 - We prove that for the N-dimensional Walsh-Fourier series the maximal operator of the Marcinkiewicz means is of weak type (1, 1). Moreover, the Marcinkiewicz means σn f of the function f ∈ L1 converge a.e. to f as n → ∞.

AB - We prove that for the N-dimensional Walsh-Fourier series the maximal operator of the Marcinkiewicz means is of weak type (1, 1). Moreover, the Marcinkiewicz means σn f of the function f ∈ L1 converge a.e. to f as n → ∞.

KW - Marcinkiewicz means

KW - Multiple Walsh-Fourier series

KW - Summability almost everywhere

UR - https://www.scopus.com/pages/publications/0242676985

UR - https://www.scopus.com/pages/publications/0242676985#tab=citedBy

U2 - 10.1016/S0022-247X(03)00503-1

DO - 10.1016/S0022-247X(03)00503-1

M3 - Article

AN - SCOPUS:0242676985

SN - 0022-247X

VL - 287

SP - 90

EP - 100

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Almost everywhere summability of multiple Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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