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Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 1, Pages 25-31
doi:10.1155/JIA.2005.25

A refinement of the Poincaré inequality for Kolmogorov operators on ℝd

Yasuhiro Fujita

Department of Mathematics, Toyama University, Toyama 930-8555, Japan

Received 28 June 2004

Abstract

We give a refinement of the Poincaré inequality for Kolmogorov operators on ℝd. This refinement yields some regularity result of the corresponding semigroups.