Compact linear combination of composition operators on Bergman-Orlicz spaces

@misc{li2026compact,
  title = {{Compact linear combination of composition operators on Bergman-Orlicz spaces}},
  author = {Yucheng Li and Zhiyu Wang and Liankuo Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28111},
  eprint = {2609.28111},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28111},
}

TY  - UNPB
TI  - Compact linear combination of composition operators on Bergman-Orlicz spaces
AU  - Yucheng Li
AU  - Zhiyu Wang
AU  - Liankuo Zhao
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28111
UR  - https://arxiv.org/abs/2609.28111
AB  - 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).
ER  -