LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on R~n. Let HAp,q （R~n） be the anisotropic Hardy-Lorentz spaces associated with A defined via the nontangential grand maximal function. In this article, the authors characterize HAp,q （R~n） in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley g*λ-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space Lp,q（R~n）. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on R~n. Moreover, the range of λ in the g*λ-function characterization of HAp,q （R~n） coincides with the best known one in the classical Hardy space Hp（R~n） or in the anisotropic Hardy space HAp （R~n）.