COMMUTATORS OF MULTILINEAR CALDERON-ZYGMUND OPERATORS WITH KERNELS OF DINI'S TYPE AND APPLICATIONS

Let T be a multilinear Calderon-Zygmund operator of type omega with omega(t) being non-decreasing and satisfying a kind of Dini's type condition. Let T-Pi(b) over right arrow be the iterated commutators of T with BMO functions. The weighted strong and weak L(logL)-type endpoint estimates for T-Pi(b) over right arrow with multiple weights are established. Some boundedness properties on weighted variable exponent Lebesgue spaces are also obtained. As applications, multiple weighted estimates for iterated commutators of bilinear pseudo-differential operators and paraproducts with mild regularity are given.