Abstract Orlicz-Morrey spaces and applications

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 $\mathrm{\Psi }$-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 $\mathrm{\Psi }$-bounded oscillation operators includes maximal operators and Carleson-type operators on general measure spaces, as well as $\omega$-Calderón-Zygmund operators and intrinsic square operators on ${\mathbb{R}}^n$, thus providing a generalization of certain classical Orlicz-Morrey spaces and their associated operator theory.