Matrix-weighted bounds in variable Lebesgue spaces
Functional Analysis
2025-09-16 v2 Classical Analysis and ODEs
Abstract
In this paper we prove boundedness of Calder\'on-Zygmund operators and the Christ-Goldberg maximal operator in the matrix-weighted variable Lebesgue spaces recently introduced by Cruz-Uribe and the second author. Our main tool to prove these bounds is through bounding a Goldberg auxiliary maximal operator. As an application, we obtain a quantitative extrapolation theorem for matrix-weighted variable Lebesgue spaces from the recent framework of directional Banach function spaces of the first author.
Cite
@article{arxiv.2503.14398,
title = {Matrix-weighted bounds in variable Lebesgue spaces},
author = {Zoe Nieraeth and Michael Penrod},
journal= {arXiv preprint arXiv:2503.14398},
year = {2025}
}
Comments
32 pages, final version, accepted for publication in Ann. Fenn. Math