Iterated commutators under a joint condition on the tuple of multiplying functions
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- by Tuomas Hytönen, Kangwei Li and Tuomas Oikari PDF
- Proc. Amer. Math. Soc. 148 (2020), 4797-4815 Request permission
Abstract:
We present a pair of joint conditions on the two functions $b_1,b_2$ strictly weaker than $b_1,b_2\in \operatorname {BMO}$ that almost characterize the $L^2$ boundedness of the iterated commutator $[b_2,[b_1,T]]$ of these functions and a Calderón-Zygmund operator $T$. Namely, we sandwich this boundedness between two bisublinear mean oscillation conditions of which one is a slightly bumped up version of the other.References
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Additional Information
- Tuomas Hytönen
- Affiliation: Department of Mathematics and Statistics, P.O. Box 68 (Pietari Kalmin katu 5), FI-00014 University of Helsinki, Finland
- Email: tuomas.hytonen@helsinki.fi
- Kangwei Li
- Affiliation: Center for Applied Mathematics, Tianjin University, Weijin Road 92, 300072 Tianjin, People’s Republic of China
- MR Author ID: 977289
- Email: kli@tju.edu.cn
- Tuomas Oikari
- Affiliation: Department of Mathematics and Statistics, P.O. Box 68 (Pietari Kalmin katu 5), FI-00014 University of Helsinki, Finland
- Email: tuomas.v.oikari@helsinki.fi
- Received by editor(s): October 4, 2019
- Received by editor(s) in revised form: March 13, 2020
- Published electronically: July 20, 2020
- Additional Notes: The first and third authors are members of the Finnish Centre of Excellence in Analysis and Dynamics Research supported by the Academy of Finland (project No. 307333).
The third author was supported by the three-year research grant 75160010 of the University of Helsinki and the Academy of Finland project No. 306901.
The first author was supported by the Academy of Finland project No. 314829. - Communicated by: Ariel Barton
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4797-4815
- MSC (2010): Primary 42B20
- DOI: https://doi.org/10.1090/proc/15101
- MathSciNet review: 4143395