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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.22509 |
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| _version_ | 1866916594528026624 |
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| author | Henríquez-Amador, Javier Álvarez, Carlos F. |
| author_facet | Henríquez-Amador, Javier Álvarez, Carlos F. |
| contents | In this note, we consider a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of the variable exponent, we provide necessary and sufficient conditions for this class of operators to be bounded and compact, respectively. In addition, we show the usefulness of the variable change to study weak compactness properties in the framework of non-standard spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the composition operator with variable integrability Henríquez-Amador, Javier Álvarez, Carlos F. Functional Analysis In this note, we consider a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of the variable exponent, we provide necessary and sufficient conditions for this class of operators to be bounded and compact, respectively. In addition, we show the usefulness of the variable change to study weak compactness properties in the framework of non-standard spaces. |
| title | On the composition operator with variable integrability |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2410.22509 |