LUSIN AREA FUNCTION AND MOLECULAR CHARACTERIZATIONS OF MUSIELAK-ORLICZ HARDY SPACES AND THEIR APPLICATIONS

Let phi : R-n x [0, infinity) -> [0, infinity) be a growth function such that phi(x, .) is nondecreasing, phi(x, 0) = 0, phi(x, t) > 0 when t > 0, lim(t ->infinity) phi(x, t) = infinity, and phi(., t) is a Muckenhoupt A(infinity)((R)n) weight uniformly in t. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space H-phi(R-n) introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the phi-Carleson measure characterization of the Musielak-Orlicz BMO-type space BMO phi(R-n), which was proved to be the dual space of H-phi(R-n) by Luong Dang Ky.