An extrapolation of operator-valued dyadic paraproducts

作者：Mei Tao^*

来源：Journal of the London Mathematical Society-Second Series, 2010, 81: 650-662.

DOI：10.1112/jlms/jdq004

We consider the dyadic paraproducts pi(phi) on T associated with an M-valued function phi. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(p)(T, L(p)(M)) for some 1 < p < infinity implies their boundedness on L(p)(T, L(p)(M)) for all 1 < p < infinity provided that phi is in an operator-valued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on L(p)(T, L(p)(M)).

• 出版日期2010-6