A weighted Hardy type inequality and its applications

Abstract

In this paper we prove a new Hardy type inequality and as a consequence we establish embedding results for a certain Sobolev space E1,p(R+n) defined on the upper half-space. Precisely, for 1<p<n we obtain an embedding from E1,p(R+n) into weighted Lebesgue spaces. In the border-line case p=n, we derive some Trudinger-Moser type inequalities, and in the case p>n we obtain a Morrey's type inequality.