A Leray-Trudinger inequality

Abstract

We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy\'s inequality in the case p = n >= 2. In this paper we provide an optimal Sobolev-type improvement of this substitute, analogous to the corresponding improvements obtained for p = 2 < n in S. Filippas and A. Tertikas (2002) [16], and for p > n >= 1 in G. Psaradakis (2012) [26]. (C) 2015 Elsevier Inc. All rights reserved.