Weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type and their applications

摘要

Given a family of operators that act like approximations of the identity, we obtain weighted estimates for the Marcinkiewicz integrals with non-smooth kernels on spaces of ho- mogeneous type. As applications of weighted estimates, we also establish the boundedness of these operators on the homogeneous Herz spaces over Euclidean spaces, and on the homoge- neous weak Herz spaces for the endpoint case. We also study the boundedness of commutators of Marcinkiewicz integrals and BMO functions on various spaces.