On the structure of Hardy-Sobolev-Maz'ya inequalities (Q1041254)

The article is concerning improvement s of the known Hardy inequality for a convex domain \(\Omega\subset\mathbb{R}^n\): \[ \int_\Omega|\nabla u|^2 dx\geq {1\over 4} \int_\Omega {|u|^2\over d(x)^2}\,dx, \] where \(u\in C^\infty_0(\Omega)\) and \(d(x)= \text{dist}(x,\partial\Omega)\). Using some results from Sobolev spaces the authors improve the above inequality for the case that \(\Omega\) is the half space \(\mathbb{R}^n_+\).