Hardy and Carleson Measure Spaces Associated with Operators on Spaces of Homogeneous Type

摘要

Let (X, d, mu) be a metric measure space with doubling property. The Hardy spaces associated with operators L were introduced and studied by many authors. All these spaces, however, were first defined by L (2)(X) functions and finally the Hardy spaces were formally defined by the closure of these subspaces of L (2)(X) with respect to Hardy spaces norms. A natural and interesting question in this context is to characterize the closure. The purpose of this paper is to answer this question. More precisely, we will introduce , the Carleson measure spaces associated with operators L, and characterize the Hardy spaces associated with operators L via , the distributions of CMOPL(x).