Sharp Rate of Average Decay of the Fourier Transform of a Bounded Set
نویسنده
چکیده
Estimates for the decay of Fourier transforms of measures have extensive applications in numerous problems in harmonic analysis and convexity including the distribution of lattice points in convex domains, irregularities of distribution, generalized Radon transforms and others. Here we prove that the spherical L-average decay rate of the Fourier transform of the Lebesgue measure on an arbitrary bounded convex set in R is
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Moduli of Continuity and Average Decay of Fourier Transforms: Two-sided Estimates and a Cantor Type Example
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