Positive Toeplitz Operators from a Harmonic Bergman-Besov space into Another

We define positive Toeplitz operators between harmonic Bergman-Besov spaces $b_{\alpha }^p$ on the unit ball of ${\mathbb{R}}^n$ for the full ranges of parameters $0<p<\mathrm{\infty }$, $\alpha \in \mathbb{R}$. 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 $b_{\alpha }^2$ to be a Schatten class operator $S_p$ in terms of averaging functions and Berezin transforms for $1\le p<\mathrm{\infty }$, $\alpha \in \mathbb{R}$. Our results extend those known for harmonic weighted Bergman spaces.