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arXiv · 1701.07763

Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces

Lucas Chaffee·David Cruz-Uribe
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Abstract

In this article we extend recent results by the first author on the necessity of $BMO$ 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 $T$, if the commutator $[b,T]$ is bounded, then the function $b$ is in $BMO$.

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Lucas Chaffee, David Cruz-Uribe. 2017-01-26. Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces. https://arxiv.org/abs/1701.07763

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