Schatten Classes and Commutator in the Two Weight Setting, I. Hilbert Transform
Potential Analysis(2024)
摘要
We characterize the Hilbert–Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten class S p result for dyadic paraproducts, where 1< p < ∞ . We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.
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关键词
Schatten class,Commutator,Hilbert transform,Weighted Besov space,Dyadic structure
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