Uncertainty principles for the Weinstein transform

Hatem Mejjaoli; Makren Salhi

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Littlewood-paley decomposition associated with the dunkl operators and paraproduct operators.

Mejjaoli, Hatem (2008)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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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...