Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 3, Pages 207-219
doi:10.1155/JIA.2005.207

General Hardy inequalities with optimal constants and remainder terms

Shen Yaotian1 and Chen Zhihui1,2

 1School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China
2Department of Mathematics, School of Science, University of Science and Technology of China, Anhui, Hefei 230026, China
Received 1 July 2003; Revised 24 December 2004

Abstract

One-dimensional Hardy inequalities with weights and remainder terms are studied. The corresponding optimal constants are discussed. Then by the process of symmetrization, Hardy inequalities with remainder terms in high-dimensional Sobolev spaces are obtained. This result gives a positive answer to the Brézis-Vázquez conjecture.