Chapter 6 - Interpolations of Poincaré and Log-Sobolev Inequalities

Abstract

This chapter studies functional inequalities with so-called additivity property that interpolates and the log-Sobolev inequality. It introduces properties of a new inequality and presents some criteria of this inequality by connecting with the F-Sobolev inequalities and by using the Hardy's inequality. The transportation cost inequality on Riemannian manifolds is also studied. The results obtained helps in verifying a concrete model on Riemannian manifold, from which the continuous changes in the inequality from the Poincaré to the log-Sobolev can be seen.