Mathematics (Sep 2024)

Orlicz Spaces and Their Hyperbolic Composition Operators

  • Mohammed Said Al Ghafri,
  • Yousef Estaremi,
  • Zhidong Huang

DOI
https://doi.org/10.3390/math12182809
Journal volume & issue
Vol. 12, no. 18
p. 2809

Abstract

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In this paper, by extending some Lp-norm inequalities to similar inequalities for Orlicz space (LΦ-norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space LΦ(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 Lp-spaces to Orlicz spaces.

Keywords