An Extrapolation of Operator Valued Dyadic Paraproducts
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چکیده
X iv :0 70 9. 42 29 v1 [ m at h. FA ] 2 6 Se p 20 07 An Extrapolation of Operator Valued Dyadic Paraproducts Tao MEI 1 Abstract We consider the dyadic paraproducts πφ on T associated with an M-valued function φ. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(T, L(M)) for some 1 < p < ∞ implies their boundedness on L(T, L(M)) for all 1 < p < ∞ provided φ is in an operator-valued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on L(T, L(M)).
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