Schatten classes and commutator in the two weight setting, I. Hilbert transform
Functional Analysis
2022-02-25 v1 Classical Analysis and ODEs
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 result for dyadic paraproducts, where . We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.
Cite
@article{arxiv.2202.11854,
title = {Schatten classes and commutator in the two weight setting, I. Hilbert transform},
author = {Michael Lacey and Ji Li and Brett D. Wick},
journal= {arXiv preprint arXiv:2202.11854},
year = {2022}
}