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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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Table of 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.