Partially by National Natural Science Foundation Funds (10701010), Key University Science Research Project of Anhui Province (KJ2011A138) and Ph. D. Science Research Fund of Anhui Normal University.
supported by National Natural Science Foundation of China (Grant No.10701010) ;the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry;supported by National Natural Science Foundation of China (Grant No.10571015) ;Research Fund for the Doctoral Program of Higher Education of China (Grant No.20050027025)
In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.