Weighted inequalities and uncertainty principles for the \boldsymbol(k,a)-generalized Fourier transform

2015/02/17 by Troels Roussau Johansen, Johansen, Troels Roussau
Mathematics · #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1502.04958

Abstract

We obtain several versions of the Hausdorff-Young and Hardy-Littlewood inequalities for the (k,a)-generalized Fourier transform recently investigated at length by Ben Saï d, Kobayashi, and Ø rsted. We also obtain a number of weighted inequalities - in particular Pitt's inequality - that have application to uncertainty principles. Specifically we obtain several analogs of the Heisenberg-Pauli-Weyl principle for L^p-functions, local Cowling-Price-type inequalities, Donoho-Stark-type inequalities and qualitative extensions. We finally use the Hausdorff-Young inequality as a means to obtain entropic uncertainty inequalities.

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