Anisotropic mixed-norm Campanato-type spaces with applications to duals of anisotropic mixed-norm Hardy spaces

Let p→∈(0,∞)n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vec {p}\in (0,\infty )^n$$\end{document} and A be a general expansive matrix on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^n$$\end{document}. 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 HAp→(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{\vec {p}}_A({\mathbb {R}}^n)$$\end{document} for any given p→∈(0,∞)n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vec {p}\in (0,\infty )^n$$\end{document}, 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).