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On functions having coincident p-norms

Giuliano Klun
Institution: 
SISSA
Location: 
A-134
Schedule: 
Friday, April 12, 2019 - 10:00
Abstract: 

In a measure space $(X,\mathcal{A},\mu)$ we consider two measurable functions $f,g:E\to\mathbb{R}$ for some $E\in\mathcal{A}$. We characterize the property of having equal $p$-norms when $p$ varies in an infinite set $P \in [1,+\infty)$. In a first theorem we consider the case of bounded functions when $P$ is unbounded with $\sum_{p\in P}(1/p)=+\infty\,$. The second theorem deals with the possibility of unbounded functions, when $P$ has a finite accumulation point in $[1,+\infty)$. 

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