ar X iv : 0 80 5 . 01 58 v 1 [ m at h . FA ] 1 M ay 2 00 8 OPERATOR - VALUED DYADIC BMO SPACES
نویسنده
چکیده
We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions B which define a bounded paraproduct on L(H). We obtain several equivalent formulations of ‖πB‖ in terms of the norm of the ”sweep” function of B or of averages of the norms of martingales transforms of B in related spaces. Furthermore, we investigate a connection between John-Nirenberg type inequalities and Carleson-type inequalities via a product formula for paraproducts and deduce sharp dimensional estimates for John-Nirenberg type inequalities.
منابع مشابه
ar X iv : 0 80 5 . 06 20 v 1 [ m at h . FA ] 6 M ay 2 00 8 EMBEDDINGS BETWEEN OPERATOR - VALUED DYADIC BMO SPACES
We investigate a scale of dyadic operator-valued BMO spaces, corresponding to the different yet equivalent characterizations of dyadic BMO in the scalar case. In the language of operator spaces, we investigate different operator space structures on the scalar dyadic BMO space which arise naturally from the different characterisations of scalar BMO. We also give sharp dimensional growth estimate...
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تاریخ انتشار 2008