MEROMORPHIC OPTIMAL DOMAIN OF VOLTERRA OPERATORS BETWEEN BERGMAN-MORREY SPACES

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 , 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 p g , prove the structural identity W g = T g (H ) + C, and give equivalence and comparison criteria for optimal domains across symbols.