Almost everywhere convergence of a subsequence of the logarithmic means of quadratical partial sums of double Walsh-Fourier series

György Gát; Ushangi Goginava

Almost everywhere convergence of a subsequence of the logarithmic means of quadratical partial sums of double Walsh-Fourier series

György Gát
, Ushangi Goginava

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

Abstract

The main aim of this paper is to prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Fourier series is of weak type (1,1) provided that the supremum in the maximal operator is taken over special indicies. The set of Walsh polynomials is dense in L₁ (I × I), so by the well-known density argument we have that t_2n (x¹, ₂) → f (x¹, x²) a.e. for all integrable two-variable functions f.

Original language	English
Pages (from-to)	173-184
Number of pages	12
Journal	Publicationes Mathematicae Debrecen
Volume	71
Issue number	1-2
Publication status	Published - 2007
Externally published	Yes

Keywords

a.e. Convergence
Double Walsh-Fourier series
Logarithmic means

ASJC Scopus subject areas

General Mathematics

Cite this

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abstract = "The main aim of this paper is to prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Fourier series is of weak type (1,1) provided that the supremum in the maximal operator is taken over special indicies. The set of Walsh polynomials is dense in L1 (I × I), so by the well-known density argument we have that t2n (x1, 2) → f (x1, x2) a.e. for all integrable two-variable functions f.",

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AU - Gát, György

AU - Goginava, Ushangi

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N2 - The main aim of this paper is to prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Fourier series is of weak type (1,1) provided that the supremum in the maximal operator is taken over special indicies. The set of Walsh polynomials is dense in L1 (I × I), so by the well-known density argument we have that t2n (x1, 2) → f (x1, x2) a.e. for all integrable two-variable functions f.

AB - The main aim of this paper is to prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Fourier series is of weak type (1,1) provided that the supremum in the maximal operator is taken over special indicies. The set of Walsh polynomials is dense in L1 (I × I), so by the well-known density argument we have that t2n (x1, 2) → f (x1, x2) a.e. for all integrable two-variable functions f.

KW - a.e. Convergence

KW - Double Walsh-Fourier series

KW - Logarithmic means

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SN - 0033-3883

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JO - Publicationes Mathematicae Debrecen

JF - Publicationes Mathematicae Debrecen

IS - 1-2

ER -

Almost everywhere convergence of a subsequence of the logarithmic means of quadratical partial sums of double Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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