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

2017/01/26 by Lucas Chaffee, David Cruz-Uribe, Chaffee, Lucas +1 · 1 citation
Mathematics · Social Sciences · #42B20 #42B35 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Polish Legal and Social Issues

paper · pdf · doi:10.48550/arxiv.1701.07763

openalex publication_date 2017/01/26 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

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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