LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

【摘要】 Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rⁿ. Let H_A^p,q （Rⁿ） be the anisotropic Hardy-Lorentz spaces associated with A defined via the nontangential grand maximal function. In this article, the authors characterize H_A^p,q （Rⁿ） 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 L_p,q（Rⁿ）. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rⁿ. Moreover, the range of λ in the g^*_λ-function characterization of H_A^p,q （Rⁿ） coincides with the best known one in the classical Hardy space H^p（Rⁿ） or in the anisotropic Hardy space H_A^p （Rⁿ）.更多还原

【Abstract】 Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rⁿ. Let H_A^p,q （Rⁿ） be the anisotropic Hardy-Lorentz spaces associated with A defined via the nontangential grand maximal function. In this article, the authors characterize H_A^p,q （Rⁿ） 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 L_p,q（Rⁿ）. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rⁿ. Moreover, the range of λ in the g^*_λ-function characterization of H_A^p,q （Rⁿ） coincides with the best known one in the classical Hardy space H^p（Rⁿ） or in the anisotropic Hardy space H_A^p （Rⁿ）.更多还原