Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces
Classical Analysis and ODEs
2017-01-27 v1
Abstract
In this article we extend recent results by the first author on the necessity of for the boundedness of commutators on the classical Lebesgue spaces. We generalize these results to a large class of Banach function spaces. We show that with modest assumptions on the underlying spaces and on the operator , if the commutator is bounded, then the function is in .
Cite
@article{arxiv.1701.07763,
title = {Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces},
author = {Lucas Chaffee and David Cruz-Uribe},
journal= {arXiv preprint arXiv:1701.07763},
year = {2017}
}