Sharp affine weighted L^p Sobolev type inequalities

We establish sharp affine weighted L^p Sobolev type inequalities by using the L_p Busemann-Petty centroid inequality proved by Lutwak, Yang, and Zhang. Our approach consists of combining the latter with a suitable family of sharp weighted L^p Sobolev type inequalities obtained by Nguyen and allows u...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019-08, Vol.372 (4), p.2753
Main Authors: J. Haddad, C. H. Jiménez, M. Montenegro
Format: Article
Language:English
Online Access:Get full text
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Summary:We establish sharp affine weighted L^p Sobolev type inequalities by using the L_p Busemann-Petty centroid inequality proved by Lutwak, Yang, and Zhang. Our approach consists of combining the latter with a suitable family of sharp weighted L^p Sobolev type inequalities obtained by Nguyen and allows us to characterize all extremizers in some cases. The new inequalities do not rely on any euclidean geometric structure.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7728