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

E. Liflyand

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

8 Scopus citations


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 languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages21
StatePublished - 2016

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Bibliographical note

Publisher Copyright:
© 2016 American Mathematical Society.


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


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