Growth properties of Fourier transforms via moduli of continuity

William O. Bray*, Mark A Pinsky

*Corresponding author for this work

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

We obtain new inequalities for the Fourier transform, both on Euclidean space, and on non-compact, rank one symmetric spaces. In both cases these are expressed as a gauge on the size of the transform in terms of a suitable integral modulus of continuity of the function. In all settings, the results present a natural corollary: a quantitative form of the Riemann-Lebesgue lemma. A prototype is given in one-dimensional Fourier analysis.

Original languageEnglish (US)
Pages (from-to)2265-2285
Number of pages21
JournalJournal of Functional Analysis
Volume255
Issue number9
DOIs
StatePublished - Nov 1 2008

Keywords

  • Bessel and Jacobi functions
  • Helgason Fourier transform
  • Spherical means
  • Symmetric space

ASJC Scopus subject areas

  • Analysis

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