A generalization of Hardy spaces on spaces of homogeneous type

摘要

This is an announcement of my recent work [10].Let X = (X,d,n) be a space of homogeneous type in the sense of Coifman and Weiss [1, 2] (see the next section for the definition). Using atoms, Coifman and Weiss [2] introduced the Hardy space HP(X), The purpose of this report is to generalize the definition of Hardy space HP(X) and prove that the generalized Hardy spaces have the same property as HP(X). Our definition includes a kind of Hardy spaces with variable exponent. The results are new even for the Kn case.