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arXiv · 1708.09471

Sharp affine weighted $L^p$ Sobolev type inequalities

Julian Haddad·Carlos Hugo Jiménez·Marcos Montenegro
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Abstract

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 in combining in a convenient way the latter one with a suitable family of sharp weighted $L^p$ Sobolev type inequalities obtained by Nguyen and allows to characterize all extremizers in some cases. The new inequalities don't rely on any euclidean geometric structure.

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Julian Haddad, Carlos Hugo Jiménez, Marcos Montenegro. 2017-08-30. Sharp affine weighted $L^p$ Sobolev type inequalities. https://arxiv.org/abs/1708.09471

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