Hardy spaces for Fourier-Bessel expansions

We study Hardy spaces for Fourier-Bessel expansions associated with Bessel operators on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$((0,1),{x^{2\nu + 1}}dx)$$\end{document} and ((0, 1), dx). We define Hardy spaces H1 as the sets of L1-functions whose maximal functions for the corresponding Poisson semigroups belong to L1. Atomic characterizations are obtained.