Uniform convergence and integrability of Fourier integrals

Mikhail Dyachenko, Elijah Liflyand, Sergey Tikhonov

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Firstly, we study the uniform convergence of cosine and sine Fourier transforms. Secondly, we obtain Pitt-Boas type results on Lp-integrability of Fourier transforms with the power weights. The solutions of both problems are written as criteria in terms of general monotone functions.

Original languageEnglish
Pages (from-to)328-338
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume372
Issue number1
DOIs
StatePublished - Dec 2010

Bibliographical note

Funding Information:
✩ The research was partially supported by the RFFI 08-01-00302, NSH-3252.2010.1, MTM 2008-05561-C02-02, and 2009 SGR 1303.

Keywords

  • Fourier integrals
  • General monotone functions
  • Uniform convergence
  • Weighted norm inequalities

Fingerprint

Dive into the research topics of 'Uniform convergence and integrability of Fourier integrals'. Together they form a unique fingerprint.

Cite this