Essential Norms of Toeplitz Operators Between Bergman Spaces in Strongly Pseudoconvex Domains

For \(0<p_1\le p_2<\infty \) $0<p_1\le p_2<\infty$ and \(\min \{\alpha _1,\alpha _2\}>-1\) $min\{{\alpha }_1,{\alpha }_2\}>-1$ , we give estimates of the essential norm of Toeplitz operator \(T_\mu ^\beta \) $T_{\mu }^{\beta }$ acting from the Bergman space \(A_{\alpha _1}^{p_1}(\Omega )\) $A_{{\alpha }_1}^{p_1}(\mathrm{\Omega })$ to \(A_{\alpha _2}^{p_2}(\Omega )\) $A_{{\alpha }_2}^{p_2}(\mathrm{\Omega })$ for a nonnegative Borel measure \(\mu \) $\mu$ on a smoothly bounded strongly pseudoconvex domain \(\Omega \subset \mathbb {C}^n\) $\mathrm{\Omega }\subset {\mathbb{C}}^n$ , where \(\beta \in \mathbb {R}\) $\beta \in \mathbb{R}$ such that \( n+1+\beta >n\max \left\{ 1,\frac{1}{p_j}\right\} +\frac{ 1+\alpha _j}{p_j}\) $n+1+\beta >nmax\left\{1,,,\frac{1}{p_j}\right\}+\frac{1+{\alpha }_j}{p_j}$ for \(j=1,2\) $j=1,2$ .