The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces III
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913472283934720 |
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| author | Neto, Paulo Mendes de Carvalho Júnior, Renato Fehlberg |
| author_facet | Neto, Paulo Mendes de Carvalho Júnior, Renato Fehlberg |
| contents | In this manuscript, we examine the continuity properties of the Riemann-Liouville fractional integral for order $α= 1/p$, where $p > 1$, mapping from $L^p(t_0, t_1; X)$ to the Banach space $BMO(t_0, t_1; X)\cap K_{(p-1)/p}(t_0, t_1; X)$. This improvement, in some sense, refines a result by Hardy-Littlewood ([12]). To achieve this, we study properties between spaces $BMO(t_0, t_1; X)$ and $K_{(p-1)/p}(t_0, t_1; X)$. Additionally, we obtained the boundedness of the fractional integral of order $α\geq 1$ from $L^1(t_0, t_1; X)$ into the Riemann-Liouville fractional Sobolev space $W^{s,p}_{RL}(t_0, t_1; X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10180 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces III Neto, Paulo Mendes de Carvalho Júnior, Renato Fehlberg Functional Analysis 26A33, 47G10, 30H35 In this manuscript, we examine the continuity properties of the Riemann-Liouville fractional integral for order $α= 1/p$, where $p > 1$, mapping from $L^p(t_0, t_1; X)$ to the Banach space $BMO(t_0, t_1; X)\cap K_{(p-1)/p}(t_0, t_1; X)$. This improvement, in some sense, refines a result by Hardy-Littlewood ([12]). To achieve this, we study properties between spaces $BMO(t_0, t_1; X)$ and $K_{(p-1)/p}(t_0, t_1; X)$. Additionally, we obtained the boundedness of the fractional integral of order $α\geq 1$ from $L^1(t_0, t_1; X)$ into the Riemann-Liouville fractional Sobolev space $W^{s,p}_{RL}(t_0, t_1; X)$. |
| title | The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces III |
| topic | Functional Analysis 26A33, 47G10, 30H35 |
| url | https://arxiv.org/abs/2408.10180 |