Lusin area function and molecular characterizations of musielak-orlicz hardy spaces and their applications

摘要

Let L: R~n × [0,∞) → [0,∞) be a growth function such that L(x, ?) is nondecreasing, L(x, 0) = 0, L(x, t) > 0 when t > 0, lim_(t→∞)L(x, t) = ∞, and L(?, t) is a Muckenhoupt A_∞(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_L(R ~n) introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the L-Carleson measure characterization of the Musielak-Orlicz BMO-type space BMO_L(R~n), which was proved to be the dual space of H_L(R~n) by Luong Dang Ky.