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

Abstract

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