Conjugate Transforms on Dyadic Group

U. Goginava; A. Saatashvili

doi:10.3103/S1068362321010027

Conjugate Transforms on Dyadic Group

U. Goginava, A. Saatashvili

United Arab Emirates University

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

Abstract

Abstract: In this paper we study the properties of the Lebesgue constant of the conjugate transforms. For conjugate Fejér means we will find necessary and sufficient condition on t for which the estimation (Formula presented.) holds. We also prove that for dyadic irrational t, L log L is the maximal Orlicz space for which the estimation (Formula presented.). is valid.

Original language	English
Pages (from-to)	9-22
Number of pages	14
Journal	Journal of Contemporary Mathematical Analysis
Volume	56
Issue number	1
DOIs	https://doi.org/10.3103/S1068362321010027
Publication status	Published - Jan 2021

Keywords

conjugate Walsh transform
convergence in norm
Martingale transform

ASJC Scopus subject areas

Analysis
Control and Optimization
Applied Mathematics

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10.3103/S1068362321010027

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AB - Abstract: In this paper we study the properties of the Lebesgue constant of the conjugate transforms. For conjugate Fejér means we will find necessary and sufficient condition on t for which the estimation (Formula presented.) holds. We also prove that for dyadic irrational t, L log L is the maximal Orlicz space for which the estimation (Formula presented.). is valid.

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KW - convergence in norm

KW - Martingale transform

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Conjugate Transforms on Dyadic Group

Abstract

Keywords

ASJC Scopus subject areas

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