A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space

Ushangi Goginava

doi:10.1515/GMJ.2011.0001

A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space

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

Abstract

Define the two dimensional diagonal Sunouchi operator where S₂ⁿ,₂ⁿ f and σ₂ⁿ f are the (2ⁿ; 2ⁿ)th cubic-partial sums and 2ⁿth Marcinkiewicz-Fejér means of a two-dimensional Walsh-Fourier series. The main aim of this paper is to prove that the operator T is bounded from the Hardy space H_1/2 to the weak L_1/2 space and is not bounded from the Hardy space H_1/2 to the space L_1/2.

Original language	English
Pages (from-to)	67-81
Number of pages	15
Journal	Georgian Mathematical Journal
Volume	18
Issue number	1
DOIs	https://doi.org/10.1515/GMJ.2011.0001
Publication status	Published - Mar 2011
Externally published	Yes

Keywords

Hardy space
Sunouchi operator
Walsh function

ASJC Scopus subject areas

General Mathematics

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10.1515/GMJ.2011.0001

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AB - Define the two dimensional diagonal Sunouchi operator where S2n,2n f and σ2n f are the (2n; 2n)th cubic-partial sums and 2nth Marcinkiewicz-Fejér means of a two-dimensional Walsh-Fourier series. The main aim of this paper is to prove that the operator T is bounded from the Hardy space H1/2 to the weak L1/2 space and is not bounded from the Hardy space H1/2 to the space L1/2.

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KW - Sunouchi operator

KW - Walsh function

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A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space

Abstract

Keywords

ASJC Scopus subject areas

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