  We prove an extension of the Stein-Weiss weighted estimates for fractional
integrals, in the context of $L^{p}$ spaces with different integrability
properties in the radial and the angular direction. In this way, the classical
estimates can be unified with their improved radial versions. A number of
consequences are obtained: in particular we deduce precised versions of
weighted Sobolev embeddings, Caffarelli-Kohn-Nirenberg estimates, and
Strichartz estimates for the wave equation, which extend the radial
improvements to the case of arbitrary functions.
