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user 124831
5
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Accepted
Luxemburg norm as argument of Young's function: $\Phi\left(\lVert f \rVert_{L^{\Phi}}\right)$
The conjectured inequality does not hold.
For a counterexample, consider $\Phi(t)=\max(t^2,t^3)$ and $\Omega=(0,1)$.
Let $f=a\chi_{(0,b)}$ for $a,b\in (0,1)$.
It can be calculated that $\|f\|_{L^\Phi …
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