On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system

György Gát; Ushangi Goginava; Károly Nagy

doi:10.1556/SScMath.2009.1099

On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system

György Gát
, Ushangi Goginava
, Károly Nagy

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

50 Citations (Scopus)

Abstract

The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H pq into Lorentz space L pq for every p > 2/3 and 0 < q. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σ _n ( f, x 1, x 2) → ( x 1, x 2) a.e. as n → ∞.

Original language	English
Pages (from-to)	399-421
Number of pages	23
Journal	Studia Scientiarum Mathematicarum Hungarica
Volume	46
Issue number	3
DOIs	https://doi.org/10.1556/SScMath.2009.1099
Publication status	Published - Sept 1 2009
Externally published	Yes

Keywords

Marcinkiewicz-Fejér means
Maximal operator
Primary 42C10
Walsh-Kaczmarz system

ASJC Scopus subject areas

General Mathematics

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10.1556/SScMath.2009.1099

Cite this

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AU - Gát, György

AU - Goginava, Ushangi

AU - Nagy, Károly

PY - 2009/9/1

Y1 - 2009/9/1

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AB - The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H pq into Lorentz space L pq for every p > 2/3 and 0 < q. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σ n ( f, x 1, x 2) → ( x 1, x 2) a.e. as n → ∞.

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KW - Maximal operator

KW - Primary 42C10

KW - Walsh-Kaczmarz system

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On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system

Abstract

Keywords

ASJC Scopus subject areas

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