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arXiv · 2609.32589

Divergence Liftings and Regular Factorizations for Metric Cotype

Yue Wang
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Abstract

We study scalar linear factorizations of coordinate antipodal differences through sign increments on finite discrete tori and the corresponding adjoint divergence liftings. On tori of side length \(2m\) with \(m\) even, the optimal regular norms of both factorizations are \(m\). Quotient-space duality identifies the optimal nonlinear lifting constant with the corresponding Banach-valued difference constant. A sharp \(L_1\) metric-cotype inequality established jointly with Cheng and Xiang then yields \(\ell_\infty^N\)-valued nonlinear liftings with a uniform bound at the sharp metric-cotype scales, whereas the optimal regular norms of the normalized scalar linear liftings grow with the dimension of the torus.

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Yue Wang. 2026-09-26. Divergence Liftings and Regular Factorizations for Metric Cotype. https://arxiv.org/abs/2609.32589

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