Estimates for multilinear commutators of generalized fractional integral operators on weighted Morrey spaces

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbb{R}^n)$ with Gaussian kernel bounds, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n$. Assume that $\vec{b}=(b_1,b_2,\cdots,b_m)$ is a finite family of locally integrable functions, then the multilinear commutators generated by $\vec{b}$ and $L^{-\alpha/2}$ is defined by \begin{equation*} L_{\vec{b}}^{-\alpha/2}f=[b_m,\cdots,[b_2,[b_1,L^{-\alpha/2}]],\cdots,]f \end{equation*} when $b_j\in BMO(w)$, $j=1,2,\cdots,m$, the authors obtain the boundedness of $L_{\vec{b}}^{-\alpha/2}$ on weighted Morrey spaces.