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Dynamics of weighted translations on Orlicz spaces

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Abstract

Let G be a locally compact group, and let \(\Phi \) be a Young function. In this paper, we give sufficient and necessary conditions for weighted translation operators on the Orlicz space \(L^\Phi (G)\) to be chaotic and topologically multiply recurrent. In particular, chaos implies multiple recurrence in our case.

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Acknowledgements

The author deeply thanks the reviewers for the careful reading, numerous helpful suggestions, and pointing out some important issues to improve this paper.

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  1. Department of Mathematics Education, National Taichung University of Education, Taichung, 403, Taiwan

    Chung-Chuan Chen

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  1. Chung-Chuan Chen
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Correspondence to Chung-Chuan Chen.

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The author is supported by Grant 107-2115-M-142-002-MY2 of Ministry of Science and Technology, Taiwan.

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Chen, CC. Dynamics of weighted translations on Orlicz spaces. Collect. Math. 71, 173–187 (2020). https://doi.org/10.1007/s13348-019-00256-3

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  • DOI: https://doi.org/10.1007/s13348-019-00256-3

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