Weighted inequalities and uncertainty principles for the $\boldsymbol{(k,a)}$-generalized Fourier transform
Abstract
We obtain several versions of the Hausdorff-Young and Hardy-Littlewood inequalities for the -generalized Fourier transform recently investigated at length by Ben Sa\"i d, Kobayashi, and {\O} 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 -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.
Keywords
Cite
@article{arxiv.1502.04958,
title = {Weighted inequalities and uncertainty principles for the $\boldsymbol{(k,a)}$-generalized Fourier transform},
author = {Troels Roussau Johansen},
journal= {arXiv preprint arXiv:1502.04958},
year = {2016}
}
Comments
Updated references, minor corrections, adjustments to range of parameters in Pitt's inequality. Final version, accepted for publication in International J. Math