Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents
Abstract
In this article, we give various real-variable properties of local Muckenhoupt matrix weights W and establish the quantitative boundedness of several operators on local matrix-weighted Lebesgue spaces Lp(W), including local (fractional) maximal operators, local fractional integral operators, local Haar square functions, and Calderón--Zygmund operators with exponential decay. For the local maximal operators, we obtain the sharp quantitative bounds when p∈(1,2], while, for local fractional integral operators, we obtain the quantitative bounds matching the global best known exponents, whose scalar case is known to be sharp. The key used strategies include giving a new extension property (which can clarify their relationships with global ones) and an optimal scale lifting property (which can balance the locality of weights and operators under consideration) of local matrix weights. As an application, we establish the quantitative boundedness on Lp(W) of the Riesz transform associated with Schrödinger operators −Δ+m2I with m∈(0,∞) being large enough, whose quantitative bound when p=2 is precisely [W]𝒜loc2(r)3/2.
Related
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- Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp L2 stability and Lp extensions
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BibTeX
@misc{hytonen2026local,
title = {{Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents}},
author = {Tuomas Hytönen and Dachun Yang and Wen Yuan and Mingdong Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19597},
eprint = {2609.19597},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19597},
}
RIS
TY - UNPB
TI - Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents
AU - Tuomas Hytönen
AU - Dachun Yang
AU - Wen Yuan
AU - Mingdong Zhang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19597
UR - https://arxiv.org/abs/2609.19597
AB - In this article, we give various real-variable properties of local Muckenhoupt matrix weights W and establish the quantitative boundedness of several operators on local matrix-weighted Lebesgue spaces L^p(W), including local (fractional) maximal operators, local fractional integral operators, local Haar square functions, and Calderón--Zygmund operators with exponential decay. For the local maximal operators, we obtain the sharp quantitative bounds when p∈(1,2], while, for local fractional integral operators, we obtain the quantitative bounds matching the global best known exponents, whose scalar case is known to be sharp. The key used strategies include giving a new extension property (which can clarify their relationships with global ones) and an optimal scale lifting property (which can balance the locality of weights and operators under consideration) of local matrix weights. As an application, we establish the quantitative boundedness on L^p(W) of the Riesz transform associated with Schrödinger operators −Δ+m^2I with m∈(0,∞) being large enough, whose quantitative bound when p=2 is precisely [W]_𝒜^loc_2(r)^3/2.
ER -