Year: 2026
Type: preprint
Abstract: Let Ψ be an Orlicz function, and let T denote any finite linear combination of composition operators. Motivated by the work of Choe, Koo, and Wang on the compactness of linear combinations of composition operators on weighted Bergman spaces, we completely characterize the compactness of T on the Bergman-Orlicz space AΨ(D). Unlike the classical weighted Bergman space setting, the precise analysis on AΨ(D) depends on the growth behavior of Ψ and the associated Luxemburg norm. Hence, the power-type estimates available in weighted Bergman spaces cannot be applied directly. To overcome this difficulty, under suitable growth assumptions on Ψ and using the Julia-Caratheodory type function theory and Carleson type measure technique, respectively, we establish two necessary and sufficient compactness characterizations for T on AΨ(D).
Source: arXiv (Cornell University)
Authors: Li, Yucheng, Wang, Zhiyu, Zhao, Liankuo
Institutions: Hebei Normal University, Shanxi Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5419885406, G7268673438
OpenAlex ID: W7214238974