Characterization of compactness of commutators of bilinear singular integral operators
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- by Lucas Chaffee, Peng Chen, Yanchang Han, Rodolfo H. Torres and Lesley A. Ward PDF
- Proc. Amer. Math. Soc. 146 (2018), 3943-3953 Request permission
Abstract:
The commutators of bilinear Calderón–Zygmund operators and pointwise multiplication with a symbol in $\mathrm {CMO}$ are bilinear compact operators on products of Lebesgue spaces. We show that, for certain non-degenerate Calderón–Zygmund operators, the symbol being in $\mathrm {CMO}$ is not only sufficient but actually necessary for the compactness of the commutators.References
Additional Information
- Lucas Chaffee
- Affiliation: Department of Mathematics, Western Washington University, 516 High Street, Bellingham, Washington 98225
- MR Author ID: 1067134
- Email: Lucas.Chaffee@wwu.edu
- Peng Chen
- Affiliation: Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guang-zhou, 510275, People’s Republic of China
- MR Author ID: 951344
- Email: chenpeng3@mail.sysu.edu.cn
- Yanchang Han
- Affiliation: School of Mathematical Sciences, South China Normal University, Guang-zhou, 510631, People’s Republic of China
- MR Author ID: 767053
- Email: hanych@scnu.edu.cn
- Rodolfo H. Torres
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- MR Author ID: 173635
- ORCID: 0000-0002-3777-8671
- Email: torres@ku.edu
- Lesley A. Ward
- Affiliation: School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes SA 5095, Australia
- MR Author ID: 614761
- Email: lesley.ward@unisa.edu.au
- Received by editor(s): September 6, 2017
- Received by editor(s) in revised form: December 9, 2017
- Published electronically: June 11, 2018
- Additional Notes: The second author was supported by NNSF of China 11501583, Guangdong Natural Science Foundation 2016A030313351, the Fundamental Research Funds for the Central Universities 161gpy45, and by the Australian Research Council, Grant No. ARC-DP160100153.
The third author was supported by Guangdong Province Natural Science Foundation Grant No. 2017A030313028.
The second and fifth authors were supported by the Australian Research Council, Grant No. ARC-DP160100153. - Communicated by: Svitlana Mayboroda
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3943-3953
- MSC (2010): Primary 42B20; Secondary 47B07, 42B35, 47G99
- DOI: https://doi.org/10.1090/proc/14050
- MathSciNet review: 3825847