Some properties of the Walsh-Nörlund means

Ushangi Goginava; Károly Nagy

doi:10.2989/16073606.2021.2014594

Some properties of the Walsh-Nörlund means

Ushangi Goginava, Károly Nagy

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

5 Citations (Scopus)

Abstract

In the present paper we give a necessary and suﬃcient condition on monotone weights, which guaranties the Nörlund means of Walsh-Fourier series converge in L ₁ norm and C_W norm. We also discuss the almost everywhere summability by Nörlund means and we prove that our condition is suﬃcient for almost everywhere convergence of Nörlund means for all integrable functions.

Original language	English
Pages (from-to)	301-334
Number of pages	34
Journal	Quaestiones Mathematicae
Volume	46
Issue number	2
DOIs	https://doi.org/10.2989/16073606.2021.2014594
Publication status	Published - 2023

Keywords

almost everywhere convergence
convergence in norm
Fejér mean
martingale transform
Nörlund mean
Walsh system
weak type inequality

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.2989/16073606.2021.2014594

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AU - Nagy, Károly

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AB - In the present paper we give a necessary and suﬃcient condition on monotone weights, which guaranties the Nörlund means of Walsh-Fourier series converge in L 1 norm and CW norm. We also discuss the almost everywhere summability by Nörlund means and we prove that our condition is suﬃcient for almost everywhere convergence of Nörlund means for all integrable functions.

KW - almost everywhere convergence

KW - convergence in norm

KW - Fejér mean

KW - martingale transform

KW - Nörlund mean

KW - Walsh system

KW - weak type inequality

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Some properties of the Walsh-Nörlund means

Abstract

Keywords

ASJC Scopus subject areas

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