Noncommutative differential transforms for averaging operators
Operator Algebras
2022-03-03 v2 Functional Analysis
Abstract
In this paper, we complete the study of mapping properties for a family of operators evaluating the difference between differentiation operators and conditional expectations acting on noncommutative -spaces. To be more precise, we establish the weak type and estimates of this difference. Consequently, in conjunction with interpolation and duality, we obtain all strong type estimates. This allows us to obtain a quick application to noncommutative differential transforms for averaging operators.
Cite
@article{arxiv.2104.08526,
title = {Noncommutative differential transforms for averaging operators},
author = {Bang Xu},
journal= {arXiv preprint arXiv:2104.08526},
year = {2022}
}
Comments
20 pages. This is the final version. To appear in Journal of Operator Theory