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arXiv · 2309.13298

A Rogers--Brascamp--Lieb--Luttinger inequality in the space of matrices

Julián Haddad
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Abstract

We consider convex bodies in $M_{n,m}(\mathbb R)$, the space of matrices of $n$-rows and $m$-columns. A special case of fiber-symmetrization in $M_{n,m}(\mathbb R)$ was recently introduced in [5,6]. We prove a Rogers--Brascamp--Lieb--Luttinger type inequality with respect to this symmetrization, for quasi-concave functions and provide some applications.

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Julián Haddad. 2023-09-23. A Rogers--Brascamp--Lieb--Luttinger inequality in the space of matrices. https://arxiv.org/abs/2309.13298

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