The preduals of Banach space valued Bourgain-Morrey spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911091314917376 |
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| author | Bai, Tengfei Guo, Pengfei Xu, Jingshi |
| author_facet | Bai, Tengfei Guo, Pengfei Xu, Jingshi |
| contents | Let $X$ be a Banach space such that there exists a Banach space $^\ast X$ and $ ( ^\ast X )^ \ast = X $. In this paper, we introduce $X$-valued Bourgain-Morrey spaces. We show that $^\ast X$-valued block spaces are the predual of $X$-valued Bourgain-Morrey spaces. We obtain the completeness, denseness and Fatou property of $^\ast X$-valued block spaces. We give a description of the dual of $X$-valued Bourgain-Morrey spaces and conclude the reflexivity of these spaces. The boundedness of powered Hardy-Littlewood maximal operator in vector valued block spaces is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The preduals of Banach space valued Bourgain-Morrey spaces Bai, Tengfei Guo, Pengfei Xu, Jingshi Functional Analysis Classical Analysis and ODEs 42B25, 42B35, 46E30 Let $X$ be a Banach space such that there exists a Banach space $^\ast X$ and $ ( ^\ast X )^ \ast = X $. In this paper, we introduce $X$-valued Bourgain-Morrey spaces. We show that $^\ast X$-valued block spaces are the predual of $X$-valued Bourgain-Morrey spaces. We obtain the completeness, denseness and Fatou property of $^\ast X$-valued block spaces. We give a description of the dual of $X$-valued Bourgain-Morrey spaces and conclude the reflexivity of these spaces. The boundedness of powered Hardy-Littlewood maximal operator in vector valued block spaces is obtained. |
| title | The preduals of Banach space valued Bourgain-Morrey spaces |
| topic | Functional Analysis Classical Analysis and ODEs 42B25, 42B35, 46E30 |
| url | https://arxiv.org/abs/2505.19143 |