Boundedness of commutators and H${}^1$-BMO duality in the two matrix weighted setting
Abstract
In this paper we characterize the two matrix weighted boundedness of commutators with any of the Riesz transforms (when both are matrix A weights) in terms of a natural two matrix weighted BMO space. Furthermore, we identify this BMO space when as the dual of a natural two matrix weighted H space, and use our commutator result to provide a converse to Bloom's matrix A theorem, which as a very special case proves Buckley's summation condition for matrix A weights. Finally, we use our results to prove a matrix weighted John-Nirenberg inequality, and we also briefly discuss the challenging question of extending our results to the matrix weighted vector BMO setting.
Keywords
Cite
@article{arxiv.1511.02926,
title = {Boundedness of commutators and H${}^1$-BMO duality in the two matrix weighted setting},
author = {Joshua Isralowitz},
journal= {arXiv preprint arXiv:1511.02926},
year = {2017}
}
Comments
v3: 36 pages, no figures, updated bibliography, typos corrected, simplified proof of b) implies a) in Theorem 2.2, to appear in the journal Integral Equations and Operator Theory