Compactness of averaging operators on Banach function spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909084752543744 |
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| author | Koshino, Katsuhisa |
| author_facet | Koshino, Katsuhisa |
| contents | Let $X$ be a Borel metric measure space such that each closed ball is of positive and finite measure. In this paper, we give a sufficient and necessary condition for averaging operators on a Banach function space $E(X)$ on $X$ to be compact. As a corollary, we show that the averaging operators on the Lorentz space $L^{p,q}(X)$ of $X$ is compact if and only if $X$ is bounded, in the case where $X$ is a doubling and Borel-regular metric measure space with some continuity between metric and measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15373 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactness of averaging operators on Banach function spaces Koshino, Katsuhisa Functional Analysis 47B01, 46E30 Let $X$ be a Borel metric measure space such that each closed ball is of positive and finite measure. In this paper, we give a sufficient and necessary condition for averaging operators on a Banach function space $E(X)$ on $X$ to be compact. As a corollary, we show that the averaging operators on the Lorentz space $L^{p,q}(X)$ of $X$ is compact if and only if $X$ is bounded, in the case where $X$ is a doubling and Borel-regular metric measure space with some continuity between metric and measure. |
| title | Compactness of averaging operators on Banach function spaces |
| topic | Functional Analysis 47B01, 46E30 |
| url | https://arxiv.org/abs/2401.15373 |