Weighted inequalities for the Riesz potential on the sphere. Issue 6 (2nd June 2016) - Arenas, A.; Ciaurri, Ó.; Labarga, E.
ABSTRACT: We prove a version of the Stein–Weiss inequality for the Riesz potential of the conformal Laplacian on the sphere. Moreover, we show that the result can be improved for functions invariant under the action of the group S O ( d − 1 ) . This last result will be a consequence of a more general one for ultraspherical expansions.