Transference method for cone–like restricted summability of the two–dimensional walsh–like systems

Károly Nagy; Mohamed Salim

doi:10.7153/mia-2021-24-16

Transference method for cone–like restricted summability of the two–dimensional walsh–like systems

Károly Nagy, Mohamed Salim

Department of Mathematical Sciences

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

Abstract

In the present paper we investigate the boundedness of the maximal operator of some d-dimensional means, provided that the set of the indeces is inside a cone-like set L. Applying some assumptions on the summation kernels P_n1_,...,nd we state that the cone-like restricted maximal operator T_CLR^γ is bounded from the Hardy space H_p^γ to the Lebesgue space Lp for p > p0 .

Original language	English
Pages (from-to)	219-234
Number of pages	16
Journal	Mathematical Inequalities and Applications
Volume	24
Issue number	1
DOIs	https://doi.org/10.7153/mia-2021-24-16
Publication status	Published - 2021

Keywords

Almost everywhere convergence
Cesàro means
Group of 2-adic integers
Hardy space
Maximal operator
Multidimensional system
Restricted summability
Walsh-Kaczmarz system
Walsh-Paley system

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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abstract = "In the present paper we investigate the boundedness of the maximal operator of some d-dimensional means, provided that the set of the indeces is inside a cone-like set L. Applying some assumptions on the summation kernels Pn1,...,nd we state that the cone-like restricted maximal operator TCLRγ is bounded from the Hardy space Hpγ to the Lebesgue space Lp for p > p0 .",

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AB - In the present paper we investigate the boundedness of the maximal operator of some d-dimensional means, provided that the set of the indeces is inside a cone-like set L. Applying some assumptions on the summation kernels Pn1,...,nd we state that the cone-like restricted maximal operator TCLRγ is bounded from the Hardy space Hpγ to the Lebesgue space Lp for p > p0 .

KW - Almost everywhere convergence

KW - Cesàro means

KW - Group of 2-adic integers

KW - Hardy space

KW - Maximal operator

KW - Multidimensional system

KW - Restricted summability

KW - Walsh-Kaczmarz system

KW - Walsh-Paley system

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JF - Mathematical Inequalities and Applications

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Transference method for cone–like restricted summability of the two–dimensional walsh–like systems

Abstract

Keywords

ASJC Scopus subject areas

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