I've been working on a paper with the aforementioned title by Caffarelli & Silvestre. But i have a difficulty in showing that $\int_{y>0} | {\nabla u}|^{2} y^{a} dX = \int_{\mathbb{R}^{n}} |\xi |^{2s} |\hat{f} (\xi)|^{2}$ . Please can anyone help me how to show that the first integral equals the second? Thanks
Christian
