Commutators of a class of Ψ-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications

@misc{shan2026commutators,
  title = {{Commutators of a class of $Ψ$-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications}},
  author = {Fate Shan and Wei Wang and Yuchen Li and Jiang Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.25517},
  eprint = {2608.25517},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.25517},
}

TY  - UNPB
TI  - Commutators of a class of Ψ-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications
AU  - Fate Shan
AU  - Wei Wang
AU  - Yuchen Li
AU  - Jiang Zhou
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2608.25517
UR  - https://arxiv.org/abs/2608.25517
AB  - In our previous work \cite{SZ2026}, we established a class of abstract Orlicz-Morrey spaces endowed with a ball-basis and introduced the notion of Ψ-bounded oscillation operators. The present paper further develops this theory by investigating sparse domination and weighted estimates for such operators and their commutators within the framework of abstract Orlicz-Morrey spaces endowed with a ball-basis. We obtain pointwise sparse domination results for the operators and establish their boundedness on weighted Orlicz-Morrey spaces. The hypotheses of these conclusions differ from those in the classical Orlicz-Morrey setting and do not rely on dyadic decompositions of Euclidean structure. Moreover, we study the duality of these spaces and prove that the dual of the associated block space is exactly the Orlicz-Morrey space under consideration.
ER  -