Abstract:
Let M be a space of homogeneous type and denote by F^\infty_{cont}(M) the space of finite linear combinations of continuous (1,\infty)atoms. In this note we give a simple function theoretic proof of the equivalence on F^\infty_{cont}(M) of the H^1norm and the norm defined in terms of finite linear combinations of atoms. The result holds also for the class of nondoubling metric measure spaces considered in previous works of A. Carbonaro and the authors.
Keywords:
Space of homogeneous type, atomic Hardy space
MSC:
42
