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arXiv · 2606.25455

Abstract Orlicz-Morrey spaces and 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 \(\Psi\)-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 \(\Psi\)-bounded oscillation operators includes maximal operators and Carleson-type operators on general measure spaces, as well as \(\omega\)-Calder\'on-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.

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F. Shan, J. Zhou. 2026-06-24. Abstract Orlicz-Morrey spaces and applications. https://arxiv.org/abs/2606.25455

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