Symmetrization inequalities and Sobolev embeddings

Martín, Joaquim; Milman, Mario

doi:10.1090/S0002-9939-06-08277-3

Symmetrization inequalities and Sobolev embeddings
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by Joaquim Martín and Mario Milman PDF

Proc. Amer. Math. Soc. 134 (2006), 2335-2347 Request permission

Abstract:

We prove new extended forms of the Pólya-Szegö symmetrization principle. As a consequence new sharp embedding theorems for generalized Besov spaces are proved, including a sharpening of the limiting cases of the classical Sobolev embedding theorem. In particular, a surprising self-improving property of certain Sobolev embeddings is uncovered.

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