Refined convex Sobolev inequalities

This paper is devoted to refinements of convex Sobolev inequalities in the case of power law relative entropies: a nonlinear entropy–entropy production relation improves the known inequalities of this type. The corresponding generalized Poincaré-type inequalities with weights are derived. Optimal constants are compared to the usual Poincaré constant. © 2005 Elsevier Inc. All rights reserved.