Displaying similar documents to “On the Fourier transform of the symmetric decreasing rearrangements”

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.

Uncertainty principles for orthonormal bases

Philippe Jaming (2005-2006)

Séminaire Équations aux dérivées partielles

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In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks...). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro. Finally, we reformulate some uncertainty principles in terms of properties of the free heat and shrödinger equations.

Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms

Adam Osękowski (2014)

Open Mathematics

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We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In particular, we obtain optimal estimates for second-order Riesz transforms, which lead to interesting a priori bounds for smooth functions on ℝd. The proofs rest on probabilistic methods: we deduce the above inequalities from the corresponding estimates for martingales. To obtain the lower bounds, we exploit the properties of laminates, important probability...