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Compactness of the Bloom sparse operators and applications

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arxiv 2204.11990 v2 pith:O55PXX6M submitted 2022-04-25 math.CA

Peng Chen , Michael Lacey , Ji Li , Manasa N. Vempati This is my paper · ORCID
classification math.CA
keywords compactnesscharacterizationoperatorsbloomhomogeneoussettingspacessparse
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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 a direct application we obtain the compactness characterization for the maximal commutators with respect to the weighted VMO functions and the commutator of Calder\'on-Zygmund operators on the homogeneous spaces. Furthermore, our approach can be applied to compactness characterization for operators in the multilinear Bloom setting.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Commutators of Maximal Operators on Weighted Morrey Spaces

    math.FA 2024-11 reject novelty 4.0 of 10

    The paper extends Euclidean BMO commutator characterizations to weighted Morrey spaces on spaces of homogeneous type, but the proofs have major gaps.

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