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- W4297835528 abstract "In the line of previous work by Naor, we establish new forms of metric $mathrm{X}_p$ inequalities in group algebras under very general assumptions. Our results' applicability goes beyond the previously known setting in two directions. In first place, we find continuous forms of the $mathrm{X}_p$ inequality in the $n$-dimensional torus. Second, we consider transferred forms of the sharp scalar valued metric $mathrm{X}_p$ inequality in the von Neumann algebra $mathcal{L}(mathrm{G})$ of a discrete group $mathrm{G}$. As a byproduct of our results, some metric consequences and their relation with bi-Lipschitz nonembeddability of Banach spaces are explored in the context of noncommutative $L_p$ spaces." @default.
- W4297835528 created "2022-10-01" @default.
- W4297835528 creator A5036632581 @default.
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- W4297835528 date "2022-09-13" @default.
- W4297835528 modified "2023-09-25" @default.
- W4297835528 title "Trigonometric chaos and $mathrm{X}_p$ inequalities II -- $mathrm{X}_p$ inequalities in group von Neumann algebras" @default.
- W4297835528 doi "https://doi.org/10.48550/arxiv.2209.05991" @default.
- W4297835528 hasPublicationYear "2022" @default.
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