Multiple fourier transforms and trigonometric series in line with Hardy’s variation

E. Liflyand

doi:10.1090/conm/659/13147

Multiple fourier transforms and trigonometric series in line with Hardy’s variation

E. Liflyand

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

9 Scopus citations

Abstract

For functions of bounded Hardy’s variation, integrability results for their Fourier transforms are presented and proved in a somewhat different way than before. In order to obtain integrability theorems for multiple trigonometric series with coefficients also of bounded Hardy’s variation, passage relations are elaborated. Unlike those known earlier, they deal only with one variation, the Hardy variation.

Original language	English
Title of host publication	Contemporary Mathematics
Publisher	American Mathematical Society
Pages	135-155
Number of pages	21
DOIs	https://doi.org/10.1090/conm/659/13147
State	Published - 2016

Publication series

Name	Contemporary Mathematics
Volume	659
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Bibliographical note

Publisher Copyright:
© 2016 American Mathematical Society.

Keywords

Bounded variation
Fourier transform
Hardy space
Hardy variation
Hilbert transform
Integrability of trigonometric series

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10.1090/conm/659/13147

Cite this

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Multiple fourier transforms and trigonometric series in line with Hardy’s variation

Abstract

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Bibliographical note

Keywords

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