AI 中文总结
本文研究赋予球基的抽象加权Orlicz-Morrey空间上Ψ有界振荡算子的交换子，得到其逐点稀疏控制结果与有界性，还证明了相关块空间的对偶性，丰富了相关空间理论。
AI 中文摘要
在我们之前的工作\uc17b{SZ2026}中，建立了一类赋予球基的抽象Orlicz-Morrey空间，并引入了Ψ有界振荡算子的概念。本文在赋予球基的抽象Orlicz-Morrey空间框架下，进一步发展该理论，研究此类算子及其交换子的稀疏控制与加权估计。我们得到了该类算子的逐点稀疏控制结果，建立了它们在加权Orlicz-Morrey空间上的有界性。这些结论的假设条件不同于经典Orlicz-Morrey情形，不依赖于欧氏结构的二进分解。此外，我们还研究了此类空间的对偶性，证明了相关块空间的对偶恰好是所考虑的Orlicz-Morrey空间。
英文摘要
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.
