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arXiv · 1505.07763

Sharp affine Sobolev type inequalities via the $\Lp$ Busemann-Petty centroid inequality

Julian Haddad·C. Hugo Jimenez·Marcos Montenegro
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Abstract

We show that the $\Lp$ Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo-Nirenberg inequalities. Our approach allows also to characterize directly the corresponding equality cases.

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Julian Haddad, C. Hugo Jimenez, Marcos Montenegro. 2015-05-28. Sharp affine Sobolev type inequalities via the $\Lp$ Busemann-Petty centroid inequality. https://doi.org/10.1016/j.jfa.2016.03.017

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