English

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 LpL_{p}-spaces. To be more precise, we establish the weak type (1,1)(1,1) and (L,BMO)(L_{\infty},\mathrm{BMO}) estimates of this difference. Consequently, in conjunction with interpolation and duality, we obtain all strong type (p,p)(p,p) estimates. This allows us to obtain a quick application to noncommutative differential transforms for averaging operators.

Keywords

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

R2 v1 2026-06-24T01:16:28.500Z