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Pitt’s Inequality and Logarithmic Uncertainty Principle for the Dunkl Transform on \({\mathbb{R}}\)

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Abstract

We establish Pitt’s inequality and deduce Beckner’s logarithmic uncertainty principle for the Dunkl transform on \({\mathbb{R}}\). Also, we prove Stein–Weiss inequality for the Dunkl–Bessel potentials.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Jazan University, P.O.Box 114, Jazan, Kingdom of Saudi Arabia

    F. Soltani

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  1. F. Soltani
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Correspondence to F. Soltani.

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Author partially supported by DGRST project 04/UR/15-02 and CMCU program 10G 1503.

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Soltani, F. Pitt’s Inequality and Logarithmic Uncertainty Principle for the Dunkl Transform on \({\mathbb{R}}\) . Acta Math. Hungar. 143, 480–490 (2014). https://doi.org/10.1007/s10474-014-0415-3

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  • DOI: https://doi.org/10.1007/s10474-014-0415-3

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