Absolute convergence of multiple Fourier integrals

Yurii Kolomoitsev, Elijah Liflyand

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of Lp integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.

Original languageEnglish
Pages (from-to)17-35
Number of pages19
JournalStudia Mathematica
Issue number1
StatePublished - 2013


  • Fourier integral
  • Fourier multiplier
  • Hardy{Steklov inequality


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