Anisotropic ball Campanato-type function spaces and their applications (Q6098391)

The paper deals with the anisotropic ball Campanato-type function spaces associated with a dilation given by \(A\), a general expansive \(n\times n\) matrix, and \(X\), a ball quasi-Banach function space of \(\mathbb{R}^n\) (following the definition included in [\textit{Y.~Sawano} et al., Diss. Math. 525, 102~p. (2017; Zbl 1392.42021)]). The authors show that these spaces are duals of anisotropic Hardy spaces \(H^{A}_X(\mathbb{R}^n)\), obtaining in this way anisotropic Littlewood-Paley function characterization of \(H^{A}_X(\mathbb{R}^n)\). Also, as applications, the authors establish several equivalent characterizations of anisotropic ball Campanato-type function spaces, which, combined with the atomic decomposition of tent spaces associated with both \(A\) and \(X\), further lead to their Carleson measure characterization. All these results have a wide range of generality and, particularly, even when they are applied to Morrey spaces and Orlicz-Slice spaces, some of the obtained results are new. Applications to the case of anisotropic Hardy-variable spaces are also included.