Compactness of the bloom sparse operators and applications
Abstract We establish the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two weight setting on the spaces of homogeneous type in the sense of Coifman and Weiss. As an application, we obtain the compactness characterization for the commutator of Calderón–Zygmund operators on the homogeneous spaces. Furthermore, our approach can be applied to proving compactness for sparse operators in the multi-linear setting.
Authors
- Michael Thoreau Lacey (ORCID: https://orcid.org/0000-0002-4808-6064)
- Manasa N. Vempati (ORCID: https://orcid.org/0000-0001-9194-5250)
- Ji Li (ORCID: https://orcid.org/0000-0003-0995-3054)
- Peng Chen (ORCID: https://orcid.org/0009-0006-4870-2716)
Institutions
- Louisiana State University (US)
- Georgia Institute of Technology (US)
- Sun Yat-sen University (CN)
- Macquarie University (AU)
Publication Details
- Journal
- Collectanea mathematica
- Published
- 2026-10-13
- DOI
- https://doi.org/10.1007/s13348-026-00523-0
- Primary Topic
- Advanced Harmonic Analysis Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- National Natural Science Foundation of China
- Natural Science Foundation of Guangdong Province