Beckner inequality on finite- and infinite-dimensional manifolds
The authors use the dimension-free Harnack inequality, the coupling method, and Bakry-Emery's argument in order to present some explicit lower bounds 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 from [\textit{F.-Y. Wang}, Ann. Probab. 27, No.~2, 653--663 (1999; Zbl 0948.58023) and \textit{J.-D. Deuschel} and \textit{D. W. Stroock}, J.~Funct. Anal. 92, No.~1, 30--48 (1990; Zbl 0705.60066)] are generalized.
scientific article; zbMATH DE number 5127382
scientific article