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arXiv · 2212.12194

Affine Hardy--Littlewood--Sobolev inequalities

Julián Haddad·Monika Ludwig
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Abstract

Sharp affine Hardy--Littlewood--Sobolev inequalities for functions on $\mathbb R^n$ are established, which are significantly stronger than (and directly imply) the sharp Hardy--Littlewood--Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu. In addition, sharp reverse inequalities for the new inequalities and the affine fractional $L^2$ Sobolev inequalities are obtained for log-concave functions on $\mathbb R^n$.

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Julián Haddad, Monika Ludwig. 2022-12-23. Affine Hardy--Littlewood--Sobolev inequalities. https://doi.org/10.4171/jems%2F1648

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