PreprintCC BY 4.0arXiv
New matrix-weighted norm inequalities and extrapolation
Abstract
In this paper, we propose a new type of matrix-weighted theory and show the corresponding Rubio de Francia extrapolation theorems by means of noncommutative maximal inequalities. We introduce a new matrix Ap condition following Volberg's geometric formulation, and characterize it via a noncommutative Hardy--Littlewood maximal inequality. We then establish a noncommutative analogue of Rubio de Francia's abstract extrapolation theorem for trace-finite von Neumann algebras. The argument extends to L∞(ℝ)⊗̅ Md(ℂ) through pointwise matrix operations. This yields the desired extrapolation results for individual operators and maximal families, with applications to matrix-weighted boundedness of Calderón--Zygmund operators.
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BibTeX
@misc{hong2026matrixweighted,
title = {{New matrix-weighted norm inequalities and extrapolation}},
author = {Guixiang Hong and Pengfei Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29118},
eprint = {2610.29118},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29118},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New matrix-weighted norm inequalities and extrapolation
AU - Guixiang Hong
AU - Pengfei Yin
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29118
UR - https://arxiv.org/abs/2610.29118
AB - In this paper, we propose a new type of matrix-weighted theory and show the corresponding Rubio de Francia extrapolation theorems by means of noncommutative maximal inequalities. We introduce a new matrix A_p condition following Volberg's geometric formulation, and characterize it via a noncommutative Hardy--Littlewood maximal inequality. We then establish a noncommutative analogue of Rubio de Francia's abstract extrapolation theorem for trace-finite von Neumann algebras. The argument extends to L_∞(ℝ)⊗̅ M_d(ℂ) through pointwise matrix operations. This yields the desired extrapolation results for individual operators and maximal families, with applications to matrix-weighted boundedness of Calderón--Zygmund operators.
ER -