LAUSR

Let $$\vec {p}\in (0,\infty )^n$$ and A be a general expansive matrix on $${\mathbb {R}}^n$$ . In this article, the authors first introduce some new anisotropic mixed-norm Campanato-type space associated with A. Then the authors prove that this Campanato-type space is the dual space of the anisotropic mixed-norm Hardy space $$H^{\vec {p}}_A({\mathbb {R}}^n)$$ for any given $$\vec {p}\in (0,\infty )^n$$ , which further implies several equivalent characterizations of this Campanato-type space. Finally, as further applications, the authors establish the Carleson measure characterization of this Campanato-type space via first introducing the anisotropic mixed-norm tent space and establishing its atomic decomposition. In particular, even when the expansive matrix A is a diagonal matrix, all these results are new and, even in this case, the obtained dual result gives a complete answer to one open question proposed by Cleanthous et al. (J Geom Anal 27: 2758–2787, 2017).