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On functions having coincident p-norms

TitleOn functions having coincident p-norms
Publication TypeJournal Article
Year of Publication2020
AuthorsKlun, G
JournalAnnali di Matematica Pura ed Applicata (1923 -)
Volume199
Pagination955-968
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: $\begin{aligned} \mu (\{x\in E:|f(x)|>\alpha \})=\mu (\{x\in E:|g(x)|>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$

URLhttps://doi.org/10.1007/s10231-019-00907-z
DOI10.1007/s10231-019-00907-z

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