Meromorphic optimal domain of Volterra operators between Bergman–Morrey spaces

Abstract We study Volterra-type operators on Bergman–Morrey spaces. First, we obtain sharp boundedness criteria between scales, identifying the exact Bloch-type regularity required of the symbol and showing that the companion operator is bounded precisely for bounded symbols. Next, we develop the holomorphic optimal domain, prove that it is a Banach space with bounded point evaluations and multiplier algebra $H^\infty $ , and establish strict inclusions as the parameters vary. Then, we introduce the meromorphic optimal domain, characterize the constant-symbol case, and show that it is a Banach space with point evaluations bounded off the zero set of the derivative. Finally, we analyze the symbol classes $W_g$ and $V_g^{p}$ , prove the structural identity $W_g=T_g(H^\infty )+\mathbb C$ , and give equivalence and comparison criteria for optimal domains across symbols.