Characterisation of \(L_p\)-norms via Hölder's inequality (Q1931567)

In a series of papers, Matkowski derived several characterizations of the \(L_p\)-norm via classical Hölder and Minkowski inequalities; see [\textit{J. Matkowski}, J. Math. Anal. Appl. 348, No. 1, 315--323 (2008; Zbl 1154.26020)] and the references cited therein. The authors of the present paper characterize \(L_{p}\)-norms on the space of integrable step functions, defined on a probability space, via a Hölder type inequality with an optimality condition.