Weighted estimates for the discrete hilbert transform

E. Liflyand

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

6 Scopus citations


The Paley-Wiener theorem states that the Hilbert transform of an integrable odd function, which is monotone on ℝ+, is integrable. In this paper we prove weighted analogs of this theorem for sequences and their discrete Hilbert transforms under the assumption of general monotonicity for an even/odd sequence.

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Number of pages11
StatePublished - 2016

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.


  • Discrete hilbert transform
  • General monotone functions and sequences
  • Hilbert transform
  • Weighted integrability


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