Beckner Inequality on Finite- and Infinite-Dimensional Manifolds*

Abstract

By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery’s argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems. In particular, some results in [1, 2] are generalized.

Keywords

Beckner inequality / Continuous spin systems / Transportation cost inequality / 47D07 / 60H10

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