A class of \(Ψ\)-bounded oscillation operators on abstract Orlicz-Morrey spaces endowed with a ball-basis and their applications
Year: 2026
Type: preprint
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 \(\mathbb{R}^n\), thus providing a generalization of certain classical Orlicz-Morrey spaces and their associated operator theory.
Source: arXiv (Cornell University)
Institution: Xinjiang University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165939586