A characterization of a nonlinear integral triangle inequality

Abstract

Let $(E,\Vert .\Vert )$ be a Banach space and let $(\Omega ,\mu )$ be a Lebesgue measure space. We characterize, for all $p>0$, measurable functions $u:\Omega \to \mathbb{R}$ 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.

arXiv commentLink to published version: http://yokohamapublishers.jp/online2/opjnca/vol22/p1165.html