Noncommutative differential transforms for averaging operators

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.

20 pages. This is the final version. To appear in Journal of Operator Theory

References in corpus (2)

• Calderón-Zygmund operators associated to matrix-valued kernels
• Noncommutative Khintchine inequalities in interpolation spaces of $L_p$-spaces