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Uncertainty principles and weighted norm inequalities. (English) Zbl 1388.42016

Cwikel, Michael (ed.) et al., Functional analysis, harmonic analysis, and image processing: a collection of papers in honor of Björn Jawerth. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2836-5/pbk; 978-1-4704-4166-1/ebook). Contemporary Mathematics 693, 55-78 (2017).
Summary: The focus of this paper is weighted uncertainty principle inequalities in harmonic analysis. We start by reviewing the classical uncertainty principle inequality, and then proceed to extensions and refinements by modifying two major results necessary to prove the classical case. These are integration by parts and the Plancherel theorem. The modifications are made by means of generalizations of Hardy’s inequality and weighted Fourier transform norm inequalities, respectively. Finally, the traditional Hilbert space formulation is given in order to construct new examples.
For the entire collection see [Zbl 1378.46003].

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Biographic References:

Jawerth, Björn
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