LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

doi:10.1016/S0252-9602(17)30115-7

Abstract

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 non-tangential 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).

Key words: Lorentz space, anisotropic Hardy-Lorentz space, expansive matrix, Calderón reproducing formula, Littlewood-Paley function

Jun LIU, Dachun YANG, Wen YUAN. LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES[J].Acta mathematica scientia,Series B, 2018, 38(1): 1-33.

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