Displaying similar documents to “Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms”

On the Fourier transform of the symmetric decreasing rearrangements

Philippe Jaming (2011)

Annales de l’institut Fourier

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Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the L 2 behavior of a Fourier transform of a function over a small set is controlled by the L 2 behavior of the Fourier transform of its symmetric decreasing rearrangement. In the L 1 case, the same is true if we further assume that the function has a support of finite measure. As...

Uncertainty principles for the Weinstein transform

Hatem Mejjaoli, Makren Salhi (2011)

Czechoslovak Mathematical Journal

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The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi's theorem, Beurling's theorem, and Donoho-Stark's uncertainty principle are obtained for the Weinstein transform.