Littlewood-Paley characterizations for Hardy spaces on spaces of homogeneous type

摘要

Let (x, d, Μ,) be a space of homogeneous type in the sense of Coifman and Weiss. Assuming that μ satisfies certain estimates from below and there exists a suitable Calderon reproducing formula in L{sup}2(X), the authors establish a Lusin-area characterization for the atomic Hardy spaces (H{sub}(at)){sup}p (X) of Coifman and Weiss for p ∈ (po, 1), where p{sub}0 = n/(n + ∈{sub}1) depends on the "dimension" n of X and the "regularity" ∈{sub}1 of the Calderon reproducing formula. Using this characterization, the authors further obtain a Littlewood-Paley (g{sub}λ){sup}* -function characterization for H{sup}P(X) when λ > n + 2n/p and the boundedness of Calderon-Zygmund operators on H{sup}P(X). The results apply, for instance, to Ahlfors n-regular metric measure spaces, Lie groups of polynomial volume growth and boundaries of some unbounded model domains of polynomial type in C{sup}N.