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A Generalization of Poincaré and Log-Sobolev Inequalities

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Abstract

A generalized Beckner-type inequality interpolating the Poincaré and the log-Sobolev inequalities is studied. This inequality possesses the additivity property and characterizes certain exponential convergence of the corresponding Markov semi-group. A correspondence between this inequality and the so-called F-Sobolev inequality is presented, with the known criteria of the latter applying also to the former. In particular, an important result of Latała and Oleszkiewicz is generalized.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, Beijing, 100875, China

    Feng-Yu Wang

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  1. Feng-Yu Wang
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Wang, FY. A Generalization of Poincaré and Log-Sobolev Inequalities. Potential Anal 22, 1–15 (2005). https://doi.org/10.1007/s11118-004-4006-8

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  • DOI: https://doi.org/10.1007/s11118-004-4006-8

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