Hardy Spaces Associated with Some Anisotropic Mixed-Norm Herz Spaces and Their Applications

2022/10/06 by Zhao, Yichun, Zhou, Jiang
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.02932

Abstract

In this paper, we introduce anisotropic mixed-norm Herz spaces K_q, a^{α, p}(\mathbb Rⁿ) and K_q, a^{α, p}(\mathbb Rⁿ) and investigate some basic properties of those spaces. Furthermore, establishing the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on the space K_q, a^{α, p}(\mathbb Rⁿ) and the space K_q, a^{α, p}(\mathbb Rⁿ). Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces also are gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spaces H K_q, a^{α, p}(\mathbb Rⁿ) and HK_q, a^{α, p}(\mathbb Rⁿ), on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators.

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