The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

Abstract

It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the upper half space H 3 R 3 is given by the Sobolev constant.This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.g(B(x, y)) ,