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

    https://doi.org/10.1142/S0129167X16500191Cited by:39 (Source: Crossref)

    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 Saïd, Kobayashi, and Ørsted. 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 Lp-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.

    AMSC: Primary: 33C52, Secondary: 26D10, Secondary: 43A15, Secondary: 43A32, Secondary: 44A15, Secondary: 46B70