Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach

We present a unified method to obtain unweighted and weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy integral trick, recovering many known results but y...

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Bibliographic Details
Published in:Mathematische annalen 2020-02, Vol.376 (1-2), p.61-102
Main Authors: Bényi, Árpád, Martell, José María, Moen, Kabe, Stachura, Eric, Torres, Rodolfo H.
Format: Article
Language:English
Subjects:
Commutators
Functionals
Hilbert transformation
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:We present a unified method to obtain unweighted and weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy integral trick, recovering many known results but yielding also numerous new ones. In particular, we solve a problem about the boundedness of the commutators of the bilinear Hilbert transform with functions in BMO .
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-019-01870-z