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

  • F. Shan
  • J. Zhou
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Abstract

This work introduces a class of abstract Orlicz-Morrey spaces endowed with a ball-basis on general measure spaces and defines the associated concept of Ψ-bounded oscillation operators. Within this framework, we establish pointwise estimates and norm inequalities for these operators via sparse domination techniques. As applications, we verify that this class of Ψ-bounded oscillation operators includes maximal operators and Carleson-type operators on general measure spaces, as well as ω-Calderón-Zygmund operators and intrinsic square operators on ℝn, thus providing a generalization of certain classical Orlicz-Morrey spaces and their associated operator theory.

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Cite

BibTeXRIS
BibTeX
@misc{shan2026class,
  title = {{A class of \(Ψ\)-bounded oscillation operators on abstract Orlicz-Morrey spaces endowed with a ball-basis and their applications}},
  author = {F. Shan and J. Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.25455},
  eprint = {2606.25455},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.25455},
}
RIS
TY  - UNPB
TI  - A class of Ψ-bounded oscillation operators on abstract Orlicz-Morrey spaces endowed with a ball-basis and their applications
AU  - F. Shan
AU  - J. Zhou
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.25455
UR  - https://arxiv.org/abs/2606.25455
AB  - This work introduces a class of abstract Orlicz-Morrey spaces endowed with a ball-basis on general measure spaces and defines the associated concept of Ψ-bounded oscillation operators. Within this framework, we establish pointwise estimates and norm inequalities for these operators via sparse domination techniques. As applications, we verify that this class of Ψ-bounded oscillation operators includes maximal operators and Carleson-type operators on general measure spaces, as well as ω-Calderón-Zygmund operators and intrinsic square operators on ℝ^n, thus providing a generalization of certain classical Orlicz-Morrey spaces and their associated operator theory.
ER  -