Reverse Carleson Measures for Hardy Spaces in the Unit Ball

Let Hp = Hp(Bd) denote the Hardy space in the open unit ball Bd of Cd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}}^{d}$$\end{document}, d ≥ 1. We characterize the reverse Carleson measures for Hp, 1 < p < ∞, that is, we describe all finite positive Borel measures μ defined on the closed ball B¯d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{B} }_{d}$$\end{document} and such that ‖f‖Hp≤c‖f‖LpB¯d,μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Vert f\Vert }_{{H}^{p}}\le c{\Vert f\Vert }_{{L}^{p}\left({\overline{B} }_{d},\mu \right)}$$\end{document}