Local Hardy spaces associated with ball quasi-Banach function spaces and their dual spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909224733245440 |
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| author | Chen, Xinyu Tan, Jian |
| author_facet | Chen, Xinyu Tan, Jian |
| contents | Let $X$ be a ball quasi-Banach function space on $\mathbb R^{n}$ and $h_{X}(\mathbb R^{n})$ the local Hardy space associated with $X$. In this paper, under some reasonable assumptions on $X$, the infinite and finite atomic decompositions for the local Hardy space $h_{X}(\mathbb R^{n})$ are established directly, without relying on the relation between $H_{X}(\mathbb R^{n})$ and $h_{X}(\mathbb R^{n})$. Moreover, we apply the finite atomic decomposition to obtain the dual space of the local Hardy space $h_{X}(\mathbb R^{n})$. Especially, the above results can be applied to several specific ball quasi-Banach function spaces, demonstrating their wide range of applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Hardy spaces associated with ball quasi-Banach function spaces and their dual spaces Chen, Xinyu Tan, Jian Functional Analysis Classical Analysis and ODEs 42B30, 42B20 Let $X$ be a ball quasi-Banach function space on $\mathbb R^{n}$ and $h_{X}(\mathbb R^{n})$ the local Hardy space associated with $X$. In this paper, under some reasonable assumptions on $X$, the infinite and finite atomic decompositions for the local Hardy space $h_{X}(\mathbb R^{n})$ are established directly, without relying on the relation between $H_{X}(\mathbb R^{n})$ and $h_{X}(\mathbb R^{n})$. Moreover, we apply the finite atomic decomposition to obtain the dual space of the local Hardy space $h_{X}(\mathbb R^{n})$. Especially, the above results can be applied to several specific ball quasi-Banach function spaces, demonstrating their wide range of applications. |
| title | Local Hardy spaces associated with ball quasi-Banach function spaces and their dual spaces |
| topic | Functional Analysis Classical Analysis and ODEs 42B30, 42B20 |
| url | https://arxiv.org/abs/2406.10841 |