Schatten classes and commutators of Riesz transform on Heisenberg group and applications
Functional Analysis
2021-09-22 v3 Classical Analysis and ODEs
Complex Variables
Abstract
We study commutators with the Riesz transforms on the Heisenberg group. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson--Wolff and Rochberg--Semmes. The method of proof extends the earlier methods, allowing us to address not just the Riesz transforms, but also the Cauchy--Szego projection and second order Riesz transforms on the Heisenberg group, among other settings.
Keywords
Cite
@article{arxiv.2107.10569,
title = {Schatten classes and commutators of Riesz transform on Heisenberg group and applications},
author = {Zhijie Fan and Michael Lacey and Ji Li},
journal= {arXiv preprint arXiv:2107.10569},
year = {2021}
}
Comments
23 pages. V2 has shorter proofs