Schatten classes of Volterra operators on Bergman-type spaces in the unit ball

<p style='text-indent:20px;'>We devote to studying the condition of a holomorphic function <inline-formula><tex-math id="M1">\begin{document}$ g $\end{document}</tex-math></inline-formula> in complex unit ball id="M2">\begin{document}$ \mathbb{B}_n so that Volterra operator id="M3">\begin{document}$ T_g:A_\alpha^2\to A_\alpha^2 belongs Schatten id="M4">\begin{document}$ p $\end{document}</tex-math></inline-formula>-class. Assuming id="M5">\begin{document}$ n\ge2 and id="M6">\begin{document}$ \alpha>-3 $\end{document}</tex-math></inline-formula>, we get following conclusions</p><p style='text-indent:20px;'>1. For id="M7">\begin{document}$ 0<p\le n id="M8">\begin{document}$ T_g\in \mathcal{S}_p(A^2_\alpha) if only id="M9">\begin{document}$ is constant. </p><p style='text-indent:20px;'>2. id="M10">\begin{document}$ n<p<\infty id="M11">\begin{document}$ p(\alpha+1)+4n>0 id="M12">\begin{document}$ if</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \int_{\mathbb{B}_n}\left((1-|w|^2)^{n+1+\alpha+2t} \int_{\mathbb{B}_n} \frac{|Rg(z)|^2 \mathrm{d} v_{\alpha+2}(z)}{|1-\langle z, w\rangle|^{2(n+1+\alpha+t)}}\right)^\frac p2 { \tau(w)} <\infty, \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where id="M13">\begin{document}$ t>\max\{\frac np-\frac{n+1+\alpha}2, \frac{n-1}2\} id="M14">\begin{document}$ \tau(w) = (1-|w|^2)^{-n-1}{ v(w)} Möbius invariant measure id="M15">\begin{document}$ $\end{document}</tex-math></inline-formula>. Here id="M16">\begin{document}$ v normalized Lebesgue on id="M17">\begin{document}$ id="M18">\begin{document}$ v( \mathbb{B}_n) 1 id="M19">\begin{document}$ v_{\alpha+2}(z) c_{\alpha+2}(1-|z|^2)^{\alpha+2} (z) with constant id="M20">\begin{document}$ c_{\alpha+2} id="M21">\begin{document}$ v_{\alpha+2}( $\end{document}</tex-math></inline-formula>.</p>