Growth properties of Fourier transforms via moduli of continuity
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.
Bessel and Jacobi functions, Helgason Fourier transform, Spherical means, Symmetric space
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 of Functional Analysis