A note on strong summability of two-dimensional Walsh-Fourier series

Ushangi Goginava; Larry Gogoladze

doi:10.1007/s10998-013-4850-7

A note on strong summability of two-dimensional Walsh-Fourier series

Ushangi Goginava
, Larry Gogoladze

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

Abstract

The paper deals with the strong summability of Marcinkiewicz means with a variable power. Let, It is shown that if A _n ↑ ∞ arbitrary slowly, there exists f ∈ C(I ²) such that lim_n→∞ H_n (f, 0, 0, A _n) = +∞. At the same time, for every f ∈ C (I ²) there exists A _n(f) ↑ ∞ such that lim_n→∞ H _n(f, x, y, A _n) = 0 uniformly on I ².

Original language	English
Pages (from-to)	211-219
Number of pages	9
Journal	Periodica Mathematica Hungarica
Volume	66
Issue number	2
DOIs	https://doi.org/10.1007/s10998-013-4850-7
Publication status	Published - Jun 2013
Externally published	Yes

Keywords

Marcinkiewicz means
strong summability
Walsh function

ASJC Scopus subject areas

General Mathematics

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10.1007/s10998-013-4850-7

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abstract = "The paper deals with the strong summability of Marcinkiewicz means with a variable power. Let, It is shown that if A n ↑ ∞ arbitrary slowly, there exists f ∈ C(I 2) such that limn→∞ Hn (f, 0, 0, A n) = +∞. At the same time, for every f ∈ C (I 2) there exists A n(f) ↑ ∞ such that limn→∞ H n(f, x, y, A n) = 0 uniformly on I 2.",

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N2 - The paper deals with the strong summability of Marcinkiewicz means with a variable power. Let, It is shown that if A n ↑ ∞ arbitrary slowly, there exists f ∈ C(I 2) such that limn→∞ Hn (f, 0, 0, A n) = +∞. At the same time, for every f ∈ C (I 2) there exists A n(f) ↑ ∞ such that limn→∞ H n(f, x, y, A n) = 0 uniformly on I 2.

AB - The paper deals with the strong summability of Marcinkiewicz means with a variable power. Let, It is shown that if A n ↑ ∞ arbitrary slowly, there exists f ∈ C(I 2) such that limn→∞ Hn (f, 0, 0, A n) = +∞. At the same time, for every f ∈ C (I 2) there exists A n(f) ↑ ∞ such that limn→∞ H n(f, x, y, A n) = 0 uniformly on I 2.

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A note on strong summability of two-dimensional Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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