Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models
Abstract
We study dimension-free Riesz transform estimates on hypercubes equipped with non-uniform product measures. For 2≤ p<∞, 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 Lp-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.
Related
- Dimension free weak-type endpoint estimates for the vectors of the Dunkl--Riesz transform
- A dimension-free weak-type (1,1) bound for the vector Riesz transform on ℝn
- Optimal distributional estimates of the multiple Hilbert transform
- Reverse Translation and Convolution Estimates in the Framework of the Mehler-Fock Transform
- Moduli of smoothness and growth of the Laguerre transform: two-sided estimates
BibTeX
@misc{lee2026dimensionfree,
title = {{Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models}},
author = {Hun Hee Lee and Zhendong Xu and Sang-gyun Youn and Hao Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24458},
eprint = {2609.24458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24458},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models
AU - Hun Hee Lee
AU - Zhendong Xu
AU - Sang-gyun Youn
AU - Hao Zhang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24458
UR - https://arxiv.org/abs/2609.24458
AB - We study dimension-free Riesz transform estimates on hypercubes equipped with non-uniform product measures. For 2≤ p<∞, 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.
ER -