Growth properties of Fourier transforms via moduli of continuity

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. © 2008 Elsevier Inc. All rights reserved.

Document Type

Article

DOI

https://doi.org/10.1016/j.jfa.2008.06.017

Keywords

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

Publication Date

11-1-2008

Journal Title

Journal of Functional Analysis

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