@article {2020, title = {On functions having coincident p-norms}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, volume = {199}, year = {2020}, pages = {955-968}, abstract = {
In a measure space $(X,{\mathcal {A}},\mu )$, we consider two measurable functions $f,g:E\rightarrow {\mathbb {R}}$, for some $E\in {\mathcal {A}}$. We prove that the property of having equal p-norms when p varies in some infinite set $P\subseteq [1,+\infty )$ is equivalent to the following condition: $\begin{aligned} \mu (\{x\in E:|f(x)|\>\alpha \})=\mu (\{x\in E:|g(x)|\>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$
}, doi = {10.1007/s10231-019-00907-z}, url = {https://doi.org/10.1007/s10231-019-00907-z}, author = {Giuliano Klun} }