Molecular Characterizations of Variable Anisotropic Hardy Spaces with Applications to Boundedness of Calderón-Zygmund Operators

2020/06/20 by Jun Liu, Liu, Jun
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2006.11509

openalex publication_date 2020/06/20 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let p(⋅): ℝⁿ→(0,∞] be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on ℝⁿ. Let H_A^p(⋅)(ℝⁿ) be the variable anisotropic Hardy space associated with A defined via the non-tangential grand maximal function. In this article, via the known atomic characterization of H_A^p(⋅)(ℝⁿ), the author establishes its molecular characterization with the known best possible decay of molecules. As an application, the author obtains a criterion on the boundedness of linear operators on H_A^p(⋅)(ℝⁿ), which is used to prove the boundedness of anisotropic Calderón-Zygmund operators on H_A^p(⋅)(ℝⁿ). In addition, the boundedness of anisotropic Calderón-Zygmund operators from H_A^p(⋅)(ℝⁿ) to the variable Lebesgue space L^p(⋅)(ℝⁿ) is also presented. All these results are new even in the classical isotropic setting.

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