Positive Toeplitz operators from a harmonic Bergman–Besov space into another

Abstract

We define positive Toeplitz operators between harmonic Bergman–Besov spaces \(b^p_\alpha \) on the unit ball of \({\mathbb {R}}^n\) for the full ranges of parameters \(0<p<\infty \), \(\alpha \in {\mathbb {R}}\). We give characterizations of bounded and compact Toeplitz operators taking one harmonic Bergman–Besov space into another in terms of Carleson and vanishing Carleson measures. We also give characterizations for a positive Toeplitz operator on \(b^{2}_{\alpha }\) to be a Schatten class operator \(S_{p}\) in terms of averaging functions and Berezin transforms for \(1\le p<\infty \), \(\alpha \in {\mathbb {R}}\). Our results extend those known for harmonic weighted Bergman spaces.