  In this paper we establish the reversed sharp Hardy-Littlewood-Sobolev (HLS
for short) inequality on the upper half space and obtain a new HLS type
integral inequality on the upper half space (extending an inequality found by
Hang, Wang and Yan in \cite{HWY2008}) by introducing a uniform approach. The
extremal functions are classified via the method of moving spheres, and the
best constants are computed. The new approach can also be applied to obtain the
classical HLS inequality and other similar inequalities.
