English

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.

Keywords

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

R2 v1 2026-06-28T22:25:30.119Z