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Orlicz Spaces and Their Hyperbolic Composition Operators

Author

Listed:
  • 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
    School of Computer Science and Applied Mathematics, University of The Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2000, South Africa)

  • Zhidong Huang

    (Huxley Building Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK)

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.

Suggested Citation

  • Mohammed Said Al Ghafri & Yousef Estaremi & Zhidong Huang, 2024. "Orlicz Spaces and Their Hyperbolic Composition Operators," Mathematics, MDPI, vol. 12(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2809-:d:1475821
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