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 language | English (US) |
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Pages (from-to) | 2265-2285 |
Number of pages | 21 |
Journal | Journal of Functional Analysis |
Volume | 255 |
Issue number | 9 |
DOIs | |
State | Published - Nov 1 2008 |
Keywords
- Bessel and Jacobi functions
- Helgason Fourier transform
- Spherical means
- Symmetric space
ASJC Scopus subject areas
- Analysis