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arXiv · 2609.24458

Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models

Hun Hee Lee·Zhendong Xu·Sang-gyun Youn·Hao Zhang
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Abstract

We study dimension-free Riesz transform estimates on hypercubes equipped with non-uniform product measures. For $2\leq p<\infty$, we prove a dimension-free Meyer inequality for the associated carré du champ, with constants independent of both the dimension and the product measure. In contrast to the uniform case, the carré-du-champ square function does not in general coincide with the unweighted Riesz square function. Under an additional boundedness assumption on the weight parameters, we further obtain dimension-free estimates for the latter. Our proof is based on a transference from the biased hypercube to a non-tracial baby Fock model. We introduce new annihilation operators and the associated Riesz transforms on the biased hypercube, and derive explicit formulas relating them to the Riesz transforms on the non-tracial baby Fock model. The main analytic ingredient is a dimension-free $L_p$-estimate for the resulting noncommutative Riesz transform, proved by a rotation argument in the spirit of Pisier and Lust-Piquard. The same analytic mechanism also yields dimension-free Riesz transform estimates on $q$-Araki--Woods algebras.

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Hun Hee Lee, Zhendong Xu, Sang-gyun Youn, Hao Zhang. 2026-09-21. Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models. https://arxiv.org/abs/2609.24458

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