Abstract
We provide a natural BMO-criterion for the L2-boundedness of Calderón-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a proof of the L2-boundedness of the commutators [Rj,b] whenever b belongs to the Bourgain's vector-valued BMO space, where Rj is the j-th Riesz transform. A common ingredient is the operator-valued Haar multiplier studied by Blasco and Pott.
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