Let \(\mu \) be a finite positive Borel measure on [0, 1) and let \(H(\mathbb {D})\) be the space of all analytic functions in the unit disc \(\mathbb {D}\) . The Cesàro-like operator \(\mathcal {C}_\mu \) is defined in \(H(\mathbb {D})\) as follows: If \(f \in H(\mathbb {D})\) , \(f(z)=\sum _{n=0}^{\infty }a_{n}z^{n} (z\in \mathbb {D})\) , then \( \mathcal {C}_\mu (f)(z)=\sum ^\infty _{n=0}\left( \mu _n\sum ^n_{k=0}a_k\right) z^n, \ z\in \mathbb {D}, \) where, for \(n\ge 0\) , \(\mu _n\) denotes the n-th moment of the measure \(\mu \) , that is, \(\mu _n=\int _{0}^{1} t^{n}d\mu (t)\) . The Cesàro-like operator \(\mathcal {C}_\mu \) has been studied in various distinct analytic function spaces recently. However, it has rarely been studied on analytic function spaces with more sophisticated structures, such as F(p, q, s) type spaces. In this article, we characterize the positive Borel measures \(\mu \) for which the operator \(\mathcal {C}_\mu \) is bounded and compact on Bergman–Morrey space \(A^{p,\lambda }\) .
