Compact bilinear operators and paraproducts revisited
Abstract We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples. We then prove compactness of bilinear paraproducts with CMO symbols by combining one of the properties of compact bilinear operators thus obtained with vanishing Carleson measure estimates and interpolation of bilinear compactness.
Authors
- Árpád Bényi (ORCID: https://orcid.org/0000-0002-8584-8849)
- Rodolfo H. Torres (ORCID: https://orcid.org/0000-0002-3777-8671)
- Tadahiro Oh (ORCID: https://orcid.org/0000-0003-2313-1145)
- Guopeng Li (ORCID: https://orcid.org/0000-0002-5014-6767)
Institutions
- University of California, Riverside (US)
- Beijing Institute of Technology (CN)
- Maxwell Institute for Mathematical Sciences (GB)
- Western Washington University (US)
- University of Edinburgh (GB)
Publication Details
- Journal
- Canadian Mathematical Bulletin
- Published
- 2024-11-22
- DOI
- https://doi.org/10.4153/s000843952400047x
- Citations
- 5
- Primary Topic
- Advanced Harmonic Analysis Research
- Type
- article
- Field-Weighted Citation Impact
- 4.88