SHARP AFFINE WEIGHTED Lp SOBOLEV TYPE INEQUALITIES

SHARP AFFINE WEIGHTED Lp SOBOLEV TYPE INEQUALITIES

We establish sharp affine weighted Lp Sobolev type inequalities by using the Lp Busemann–Petty centroid inequality proved by Lutwak, Yang, and Zhang. Our approach consists of combining the latter with a suitable family of sharp weighted Lp Sobolev type inequalities obtained by Nguyen and allows us t...

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Veröffentlicht in:Transactions of the American Mathematical Society 2019-08, Vol.372 (4 (1019)), p.2753-2776
Hauptverfasser: HADDAD, J., JIMÉNEZ, C. H., MONTENEGRO, M.
Format: Artikel
Sprache:eng
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Zusammenfassung:We establish sharp affine weighted Lp Sobolev type inequalities by using the Lp Busemann–Petty centroid inequality proved by Lutwak, Yang, and Zhang. Our approach consists of combining the latter with a suitable family of sharp weighted Lp 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