Boundedness of Composition Operators in Orlicz–Morrey Spaces

Abstract

ABSTRACT In this paper, we investigate the necessary and sufficient conditions for the boundedness of composition operators on Orlicz–Morrey spaces. Our results encompass Lebesgue and generalized Morrey spaces as special cases. In addition, we characterize the boundedness of composition operators on weak Orlicz–Morrey spaces, which include the Orlicz–Morrey spaces. The key point of the proof is to identify the functions defining Orlicz–Morrey spaces, namely, Young functions and growth functions (see Definitions 1.1 and 1.5). Furthermore, our results also yield examples beyond the power‐type Young function setting. In particular, as discussed in Remark 1.10(iii), by choosing appropriate growth and Young functions, one obtains Orlicz–Morrey spaces whose defining Young function is not a power function. This observation also confirms that our approach genuinely generalizes the Morrey spaces established in Hatano et al. [ Journal of Inequalities and Applications 2021, no. 69 (2021): 1–15].