Year: 2026
Type: article
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.
Source: Canadian Mathematical Bulletin
Authors: Junming Liu, Jihua Sun
Institution: Guangdong University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7128999675
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