Calderón-Zygmund inequalities, Riesz potentials and Riesz transforms in weighted Sobolev spaces

In a previous work, we established a complete set of isomorphisms for the Laplace operator in weighted Sobolev spaces. We derive here some applications of these results. In particular, we obtain inequalities similar to those of Calderón-Zygmund and continuity properties of Riesz potentials and transforms in weighted Sobolev spaces. Finally, we give an application to the asymptotic behaviour of the solution of the heat equation.