Weighted Hardy-Littlewood-Sobolev inequalities on the upper half space

摘要

In this paper, we establish a weighted Hardy-Littlewood-Sobolev (HLS) inequality on the upper half space using a weighted Hardy type inequality on the upper half space with boundary term, and discuss the existence of extremal functions based on symmetrization argument. As an application, we can show a weighted Sobolev-Hardy trace inequality with p-biharmonic operator.