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Let $p(\cdot):\ {\mathbb{R}^n}\to(0,\infty)$ be a variable exponent functionsatisfying the globally log-H\"{o}lder continuous condition and $A$ a generalexpansive matrix on ${\mathbb{R}^n}$. In this article, the authors introducethe anisotropic variable Campanato-type spaces and give some applications.Especially, using the known atom and finite atom characterizations ofanisotropic variable Hardy space $H_A^{p(\cdot)}(\mathbb{R}^n)$, the authorsprove that this Campanato-type space is the appropriate dual space of$H_A^{p(\cdot)} (\mathbb{R}^n)$ with full range $p(\cdot)$. As applications,the authors first deduce several equivalent characterizations of theseCampanato-type spaces. Furthermore, the authors also introduce the anisotropicvariable tent spaces and show their atomic decomposition. Combining this andthe obtained dual theorem, the Carleson measure characterizations of theseanisotropic variable Campanato-type spaces are established.

Anisotropic Variable Campanato-Type Spaces and Their Carleson Measure Characterizations