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arXiv · 1105.5930

Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrability

Piero D'Ancona·Renato Luca'
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Abstract

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.

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Piero D'Ancona, Renato Luca'. 2011-05-31. Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrability. https://arxiv.org/abs/1105.5930

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