Anisotropic Local Hardy Spaces

In this paper we introduce and study the anisotropic local Hardy spaces \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$h_{A}^{p}(\mathbb{R}^{n})$\end{document} 0<p≤1, associated with the expansive matrix A. We obtain an atomic characterization of the distributions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$h_{A}^{p}(\mathbb{R}^{n})$\end{document}. Also we describe the dual spaces of our local Hardy anisotropic spaces as anisotropic Campanato type spaces.