Weighted Sobolev inequalities for the Riesz potentials and transforms. (Q976621)

Thanks to isomorphism results for Laplace's operator in weighted Sobolev spaces, some applications are derived. Various related spaces, intersection of Hardy spaces and weighted Sobolev spaces, are also considered. It is shown that the Riesz potentials spaces, consisting of all Riesz potentials \(I_\alpha \) of order \(\alpha \) of \(L^p\) functions, with \(1<p<\infty \), are equivalent to some appropriate weighted Sobolev spaces. Weighted inequalities for Riesz potentials are discussed thoroughly.