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arXiv · 2104.08526

Noncommutative differential transforms for averaging operators

Bang Xu
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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 $(L_{\infty},\mathrm{BMO})$ 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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Bang Xu. 2021-04-17. Noncommutative differential transforms for averaging operators. https://arxiv.org/abs/2104.08526

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