Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series

György Gát; Ushangi Goginava; Grigori Karagulyan

doi:10.1007/s10476-014-0401-6

Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series

György Gát
, Ushangi Goginava
, Grigori Karagulyan

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

13 Citations (Scopus)

Abstract

In this paper we study the a.e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. In particular, we prove the a.e. relation (Formula presented) 0 for every two-dimensional functions belonging to L log L and q > 0. From the theorem of Getsadze [7] it follows that the space L log L cannot be enlarged with preserving this strong summability property.

Original language	English
Pages (from-to)	243-266
Number of pages	24
Journal	Analysis Mathematica
Volume	40
Issue number	4
DOIs	https://doi.org/10.1007/s10476-014-0401-6
Publication status	Published - Dec 2014
Externally published	Yes

ASJC Scopus subject areas

Analysis
General Mathematics

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abstract = "In this paper we study the a.e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. In particular, we prove the a.e. relation (Formula presented) 0 for every two-dimensional functions belonging to L log L and q > 0. From the theorem of Getsadze [7] it follows that the space L log L cannot be enlarged with preserving this strong summability property.",

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AU - Goginava, Ushangi

AU - Karagulyan, Grigori

PY - 2014/12

Y1 - 2014/12

N2 - In this paper we study the a.e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. In particular, we prove the a.e. relation (Formula presented) 0 for every two-dimensional functions belonging to L log L and q > 0. From the theorem of Getsadze [7] it follows that the space L log L cannot be enlarged with preserving this strong summability property.

AB - In this paper we study the a.e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. In particular, we prove the a.e. relation (Formula presented) 0 for every two-dimensional functions belonging to L log L and q > 0. From the theorem of Getsadze [7] it follows that the space L log L cannot be enlarged with preserving this strong summability property.

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Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series

Abstract

ASJC Scopus subject areas

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