期刊
JOURNAL OF FUNCTIONAL ANALYSIS
卷 255, 期 9, 页码 2265-2285出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2008.06.017
关键词
Symmetric space; Helgason Fourier transform; Spherical means; Bessel and Jacobi functions
类别
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. (C) 2008 Elsevier Inc. All rights reserved.
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