Extrapolation and Factorization of matrix weights
Abstract
In this paper we prove the Jones factorization theorem and the Rubio de Francia extrapolation theorem for matrix weights. These results answer longstanding open questions in the study of matrix weights. The proof requires the development of the theory of convex-set valued functions and measurable seminorm functions. In particular, we define a convex-set valued version of the Hardy Littlewood maximal operator and construct an appropriate generalization of the Rubio de Francia iteration algorithm, which is central to the proof of both results in the scalar case.
Keywords
Cite
@article{arxiv.2210.09443,
title = {Extrapolation and Factorization of matrix weights},
author = {Marcin Bownik and David Cruz-Uribe},
journal= {arXiv preprint arXiv:2210.09443},
year = {2025}
}
Comments
This version expands the discussion of applying matrix extrapolation in a new section (Section 10) and gives an example by applying it to maximal singular integrals. An major typo and several lacunae in the proofs of Theorems 1.4 and 10.1 have been corrected