An operator-valued $T1$ theory for symmetric CZOs
Classical Analysis and ODEs
2019-07-26 v1 Functional Analysis
Operator Algebras
Abstract
We provide a natural BMO-criterion for the -boundedness of Calder\'on-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a proof of the -boundedness of the commutators whenever belongs to the Bourgain's vector-valued BMO space, where is the -th Riesz transform. A common ingredient is the operator-valued Haar multiplier studied by Blasco and Pott.
Keywords
Cite
@article{arxiv.1907.10791,
title = {An operator-valued $T1$ theory for symmetric CZOs},
author = {Guixiang Hong and Honghai Liu and Tao Mei},
journal= {arXiv preprint arXiv:1907.10791},
year = {2019}
}