WEIGHTED ESTIMATES FOR SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS AND APPLICATIONS

Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, two weighted estimates related to A(infinity) weights are established for singular integral operators with nonsmooth kernels via a new sharp maximal operator associated with a generalized approximation to the identity. As applications, the weighted L-p(X) and weighted endpoint estimates with general weights are obtained for singular integral operators with nonsmooth kernels, their commutators with BMO (X) functions, and associated maximal operators. Some applications to holomorphic functional calculi of elliptic operators and Schrodinger operators are also presented.