Almost everywhere convergence of (C, α)-means of quadratical partial sums of double vilenkin-fourier series

György Gát; Ushangi Goginava

doi:10.1515/GMJ.2006.447

Almost everywhere convergence of (C, α)-means of quadratical partial sums of double vilenkin-fourier series

György Gát
, Ushangi Goginava

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

12 Citations (Scopus)

Abstract

We prove that the maximal operator of the (C, α)-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1). Moreover, the (C, α)-means t^α_nf of a function f ε L¹ converge a.e. to f as n → ∞.

Original language	English
Pages (from-to)	447-462
Number of pages	16
Journal	Georgian Mathematical Journal
Volume	13
Issue number	3
DOIs	https://doi.org/10.1515/GMJ.2006.447
Publication status	Published - 2006
Externally published	Yes

Keywords

a.e. convergence
Cesáro means
Vilenkin system

ASJC Scopus subject areas

General Mathematics

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10.1515/GMJ.2006.447

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title = "Almost everywhere convergence of (C, α)-means of quadratical partial sums of double vilenkin-fourier series",

abstract = "We prove that the maximal operator of the (C, α)-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1). Moreover, the (C, α)-means tαnf of a function f ε L1 converge a.e. to f as n → ∞.",

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author = "Gy{\"o}rgy G{\'a}t and Ushangi Goginava",

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T1 - Almost everywhere convergence of (C, α)-means of quadratical partial sums of double vilenkin-fourier series

AU - Gát, György

AU - Goginava, Ushangi

PY - 2006

Y1 - 2006

N2 - We prove that the maximal operator of the (C, α)-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1). Moreover, the (C, α)-means tαnf of a function f ε L1 converge a.e. to f as n → ∞.

AB - We prove that the maximal operator of the (C, α)-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1). Moreover, the (C, α)-means tαnf of a function f ε L1 converge a.e. to f as n → ∞.

KW - a.e. convergence

KW - Cesáro means

KW - Vilenkin system

UR - https://www.scopus.com/pages/publications/84973881499

UR - https://www.scopus.com/pages/publications/84973881499#tab=citedBy

U2 - 10.1515/GMJ.2006.447

DO - 10.1515/GMJ.2006.447

M3 - Article

AN - SCOPUS:84973881499

SN - 1072-947X

VL - 13

SP - 447

EP - 462

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

IS - 3

ER -

Almost everywhere convergence of (C, α)-means of quadratical partial sums of double vilenkin-fourier series

Abstract

Keywords

ASJC Scopus subject areas

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