鞅的矩型极大算子的若干不等式

Some Inequalities of Maximal Operators of Matrix Type for Martingales

给出了算子T=∑_(n=1)~∞T_n在H_B^p和BMO_(p,B)^-上有界的一些充分条件,其中T_n(n∈P)为具有Δ性质的算子.作为应用,借助于算子值鞅变换得到了关于鞅的矩型极大算子的强(p,p)型不等式和弱(1,1)型不等式,以及其在BMO_(p,B)^-上的有界性.这些结果与经典H^p鞅论中极大算子的性质相对应.

In this paper, some sufficient conditions are given for an operator T =∑n=1^∞ T n to be bounded on HB^p and BMOp,B^-, where Tn （n ∈ P） are operators with property △. As applications, with the help of operator-valued martingale transforms, the strong （p,p） type, weak （1, 1） type inequalities and the boundedness on BMOp,B^- for maximal operators of matrix type are obtained. The results are counterparts for maximal operators in classical martingale Hp theory.