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