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We consider convex bodies in \(\operatorname {M}_{n,m}(\mathbb {R})\) , the space of matrices of n-rows and m-columns. A special case of fiber-symmetrization in \(\operatorname {M}_{n,m}(\mathbb {R})\) was recently introduced in Haddad et al. (Affine isoperimetric inequalities for higher-order projection and centroid bodies, 2023; General higher order Lp isoperimetric and Sobolev inequalities, 2023). We prove a Rogers–Brascamp–Lieb–Luttinger type inequality with respect to this symmetrization and provide some applications.

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A Rogers–Brascamp–Lieb–Luttinger Inequality in the Space of Matrices

  • 会议论文

  • 发表日期：

    2026年

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  • Julián Haddad

摘要

We consider convex bodies in \(\operatorname {M}_{n,m}(\mathbb {R})\) , the space of matrices of n-rows and m-columns. A special case of fiber-symmetrization in \(\operatorname {M}_{n,m}(\mathbb {R})\) was recently introduced in Haddad et al. (Affine isoperimetric inequalities for higher-order projection and centroid bodies, 2023; General higher order Lp isoperimetric and Sobolev inequalities, 2023). We prove a Rogers–Brascamp–Lieb–Luttinger type inequality with respect to this symmetrization and provide some applications.