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| Main Author: | |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1711.11021 |
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| _version_ | 1866916118886612992 |
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| author | Abdelhakim, Ahmed A. |
| author_facet | Abdelhakim, Ahmed A. |
| contents | Let $(E,\|.\|)$ be a Banach space and let $(Ω,μ)$ be a Lebesgue measure space. We characterize, for all $p>0$, measurable functions $u:Ω\rightarrow \mathbb{R}$ for which \begin{equation*} \left\| \int_Ω f\,dμ\right\|^{p}\,\leq\,\int_Ω u \| f \|^{p}\,dμ.\tag{I} \end{equation*} We characterize $u$ for the reverse of (I) as well. The discrete counterpart of this problem is also solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_11021 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A characterization of a nonlinear integral triangle inequality Abdelhakim, Ahmed A. Functional Analysis 47A30, 52A40, 26D15 Let $(E,\|.\|)$ be a Banach space and let $(Ω,μ)$ be a Lebesgue measure space. We characterize, for all $p>0$, measurable functions $u:Ω\rightarrow \mathbb{R}$ for which \begin{equation*} \left\| \int_Ω f\,dμ\right\|^{p}\,\leq\,\int_Ω u \| f \|^{p}\,dμ.\tag{I} \end{equation*} We characterize $u$ for the reverse of (I) as well. The discrete counterpart of this problem is also solved. |
| title | A characterization of a nonlinear integral triangle inequality |
| topic | Functional Analysis 47A30, 52A40, 26D15 |
| url | https://arxiv.org/abs/1711.11021 |