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A question left over from this post is:

Are the $L^p$ norms ordered by $p$ like the power means are?

Community
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Eric Auld
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    Depends on interpretation. The ordering of norms can be understood as $|f|p\le |f|_q$ for $p\le q$. This requires $\int\Omega dx\le 1$. If understood in the weaker sense $|f|p\le C{p,q}|f|_q$ for $p\le q$, then as in mookid's answer. – user127096 Mar 15 '14 at 17:49

1 Answers1

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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).

mookid
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