Variations on the theorems of F. and M. Riesz and of Hardy and Littlewood

Elijah Liflyand

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A function f with bounded variation and integrable Hilbert transform of df is locally absolutely continuous. We give a direct real-valued proof of this result and connect it with integrability problems for the Fourier transform of a function with bounded variation, in particular, with a Hardy-Littlewood theorem.

Original languageEnglish
Pages (from-to)337-341
Number of pages5
JournalGeorgian Mathematical Journal
Volume21
Issue number3
DOIs
StatePublished - 1 Sep 2014

Bibliographical note

Publisher Copyright:
© 2014 by De Gruyter 2014.

Keywords

  • Absolute continuity
  • Fourier transform
  • HardyLittlewood theorem
  • Hilbert transform
  • bounded variation
  • measure
  • theorem of the brothers Riesz

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