Anisotropic Variable Campanato-Type Spaces and Their Carleson Measure Characterizations

2021/12/22 by Long Huang, Huang, Long, Xiao Feng Wang +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2112.11653

openalex publication_date 2021/12/22 · openalex created_date 2022/10/07 · 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. In this article, the authors introduce the anisotropic variable Campanato-type spaces and give some applications. Especially, using the known atom and finite atom characterizations of anisotropic variable Hardy space H_A^p(⋅)(ℝⁿ), the authors prove that this Campanato-type space is the appropriate dual space of H_A^p(⋅) (ℝⁿ) with full range p(⋅). As applications, the authors first deduce several equivalent characterizations of these Campanato-type spaces. Furthermore, the authors also introduce the anisotropic variable tent spaces and show their atomic decomposition. Combining this and the obtained dual theorem, the Carleson measure characterizations of these anisotropic variable Campanato-type spaces are established.

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