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It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality onthe three dimensional upper half space is given by the Sobolev constant. Thisis achieved by a duality argument relating the problem to aHardy-Littlewood-Sobolev type inequality whose sharp constant is determined aswell.

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