Carleson Measures for Weighted Harmonic Mixed-Norm Spaces and Toeplitz Operators

We characterize Carleson measures for weighted harmonic mixed norm spaces B alpha p,q(Omega)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B<^>{p,q}_\alpha (\Omega )$$\end{document} of harmonic functions on smoothly bounded domains in 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} for a certain range of parameters p, q and alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}. This result extends earlier characterization obtained by the second author to a wider range of parameters. Also, we characterize vanishing Carleson measures for these spaces and apply these results to obtain criteria for boundedness and compactness of Toeplitz operators on weighted mixed norm spaces.