Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications
In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do...