LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

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

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 1-33.doi: 10.1016/S0252-9602(17)30115-7

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LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

刘军, 杨大春, 袁文

Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

收稿日期:2016-09-18 修回日期:2017-08-14 出版日期:2018-02-25 发布日期:2018-02-25
通讯作者: Dachun YANG E-mail:dcyang@bnu.edu.cn
作者简介:Jun LIU,E-mail:junliu@mail.bnu.edu.cn;Wen YUAN,E-mail:wenyuan@bnu.edu.cn
基金资助:
The second author was supported by the National Natural Science Foundation of China (11571039 and 11671185). The third author was supported by the National Natural Science Foundation of China (11471042).

LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

Jun LIU, Dachun YANG, Wen YUAN

Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received:2016-09-18 Revised:2017-08-14 Online:2018-02-25 Published:2018-02-25
Contact: Dachun YANG E-mail:dcyang@bnu.edu.cn
Supported by:
The second author was supported by the National Natural Science Foundation of China (11571039 and 11671185). The third author was supported by the National Natural Science Foundation of China (11471042).

摘要/Abstract

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 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).

关键词: Lorentz space, anisotropic Hardy-Lorentz space, expansive matrix, Calderón reproducing formula, Littlewood-Paley function

Abstract:

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

刘军, 杨大春, 袁文. LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 1-33.

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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LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

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