Sharp affine weighted 𝐿^{𝑝} Sobolev type inequalities

Haddad, J.; Jiménez, C.; Montenegro, M.

doi:10.1090/tran/7728

Sharp affine weighted $L^p$ Sobolev type inequalities
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by J. Haddad, C. H. Jiménez and M. Montenegro PDF

Trans. Amer. Math. Soc. 372 (2019), 2753-2776 Request permission

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 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.

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