Orlicz Spaces and Their Hyperbolic Composition Operators

Mohammed Said Al Ghafri, Yousef Estaremi () and Zhidong Huang
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Mohammed Said Al Ghafri: Department of Mathematics, University of Technology and Applied Sciences, Rustaq 329, Oman
Yousef Estaremi: Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 4934174515, Iran
Zhidong Huang: Huxley Building Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK

Mathematics, 2024, vol. 12, issue 18, 1-15

Abstract: In this paper, by extending some L p -norm inequalities to similar inequalities for Orlicz space ( L Φ -norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space L Φ ( μ ) . Additionally, we show that for composition operators on Orlicz spaces, the concepts of generalized hyperbolicity and the shadowing property are equivalent. These results extend similar findings on L p -spaces to Orlicz spaces.

Keywords: shadowing property; hyperbolicity; dissipative systems; Orlicz spaces; composition operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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