Symmetrization inequalities and Sobolev embeddings

Martín, Joaquim; Milman, Mario

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

Symmetrization inequalities and Sobolev embeddings

Authors: Joaquim Martín and Mario Milman
Journal: Proc. Amer. Math. Soc. 134 (2006), 2335-2347
MSC (2000): Primary 46E30, 26D10
DOI: https://doi.org/10.1090/S0002-9939-06-08277-3
Published electronically: February 6, 2006
MathSciNet review: 2213707
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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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