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Dimension-free weak (1,1) estimates for Riesz transforms with constant drift
Abstract
Let Lv=−Δ−2v·∇ on L2(ℝn,e2v· x dx), where v∈ℝn∖{0} is a constant drift vector. We prove that the full vector Riesz transform ∇ Lv−1/2 satisfies a weak-type (1,1) estimate for real-valued functions with constant at most $2$, uniformly in both the dimension and the drift vector. Our proof extends the fractional obstacle method of Ouyang, Spector and Stockdale (https://arxiv.org/abs/2608.18068) to the exponentially weighted setting. Interpolation then yields strong Lp bounds for 1<p≤ 2, with constants depending only on p.
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BibTeX
@misc{mukherjee2026dimensionfree,
title = {{Dimension-free weak $(1,1)$ estimates for Riesz transforms with constant drift}},
author = {Suman Mukherjee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21458},
eprint = {2609.21458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21458},
}
RIS
TY - UNPB
TI - Dimension-free weak (1,1) estimates for Riesz transforms with constant drift
AU - Suman Mukherjee
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.21458
UR - https://arxiv.org/abs/2609.21458
AB - Let L_v=−Δ−2v·∇ on L^2(ℝ^n,e^2v· x dx), where v∈ℝ^n∖{0} is a constant drift vector. We prove that the full vector Riesz transform ∇ L_v^−1/2 satisfies a weak-type (1,1) estimate for real-valued functions with constant at most $2$, uniformly in both the dimension and the drift vector. Our proof extends the fractional obstacle method of Ouyang, Spector and Stockdale (https://arxiv.org/abs/2608.18068) to the exponentially weighted setting. Interpolation then yields strong L^p bounds for 1<p≤ 2, with constants depending only on p.
ER -