Noncommutative differential transforms for averaging operators

2021/04/17 by Xu, Bang
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2104.08526

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

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