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
Recommended Citation
Bray, William O., and Mark A. Pinsky. "Growth properties of Fourier transforms via moduli of continuity." Journal of Functional Analysis 255, no. 9 (2008): 2265-2285.
Journal Title
Journal of Functional Analysis
