A question left over from this post is:
Are the $L^p$ norms ordered by $p$ like the power means are?
2026-03-27 14:10:48.1774620648
Are the $L^p$ norms ordered by $p$?
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If $\int_\Omega dx = 1$, then the Hölder inequality states that yes.
If $\int_\Omega dx <\infty$, then the Hölder inequality states that there is domination between the norms.
Otherwise, no (more details).