English

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 BMOBMO 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 TT, if the commutator [b,T][b,T] is bounded, then the function bb is in BMOBMO.

Keywords

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}
}