On the boundedness of the maximal operators of double Walsh-logarithmic means of Marcinkiewicz type

Ushangi Goginava; Károly Nagy

doi:10.2478/s12175-013-0138-x

On the boundedness of the maximal operators of double Walsh-logarithmic means of Marcinkiewicz type

Ushangi Goginava
, Károly Nagy

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

Abstract

The main aim of this paper is to investigate the (H_p, L_p)-type inequality for the maximal operators of Riesz and Nörlund logarithmic means of the quadratical partial sums of Walsh-Fourier series. Moreover, we show that the behavior of Nörlund logarithmic means is worse than the behavior of Riesz logarithmic means in our special sense.

Original language	English
Pages (from-to)	839-848
Number of pages	10
Journal	Mathematica Slovaca
Volume	63
Issue number	4
DOIs	https://doi.org/10.2478/s12175-013-0138-x
Publication status	Published - Aug 2013
Externally published	Yes

Keywords

double Walsh-Fourier series
Hardy space
logarithmic means
Nörlund means
Walsh system

ASJC Scopus subject areas

General Mathematics

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10.2478/s12175-013-0138-x

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abstract = "The main aim of this paper is to investigate the (Hp, Lp)-type inequality for the maximal operators of Riesz and N{\"o}rlund logarithmic means of the quadratical partial sums of Walsh-Fourier series. Moreover, we show that the behavior of N{\"o}rlund logarithmic means is worse than the behavior of Riesz logarithmic means in our special sense.",

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AU - Nagy, Károly

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N2 - The main aim of this paper is to investigate the (Hp, Lp)-type inequality for the maximal operators of Riesz and Nörlund logarithmic means of the quadratical partial sums of Walsh-Fourier series. Moreover, we show that the behavior of Nörlund logarithmic means is worse than the behavior of Riesz logarithmic means in our special sense.

AB - The main aim of this paper is to investigate the (Hp, Lp)-type inequality for the maximal operators of Riesz and Nörlund logarithmic means of the quadratical partial sums of Walsh-Fourier series. Moreover, we show that the behavior of Nörlund logarithmic means is worse than the behavior of Riesz logarithmic means in our special sense.

KW - double Walsh-Fourier series

KW - Hardy space

KW - logarithmic means

KW - Nörlund means

KW - Walsh system

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On the boundedness of the maximal operators of double Walsh-logarithmic means of Marcinkiewicz type

Abstract

Keywords

ASJC Scopus subject areas

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