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arXiv · 2202.11854

Schatten classes and commutator in the two weight setting, I. Hilbert transform

Michael Lacey·Ji Li·Brett D. Wick
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Abstract

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 < \infty $. We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.

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Michael Lacey, Ji Li, Brett D. Wick. 2022-02-24. Schatten classes and commutator in the two weight setting, I. Hilbert transform. https://arxiv.org/abs/2202.11854

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