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H\"older inequality

Keywords: 
vector, norm
Synonym: 
Holder inequality, Hoelder inequality
Type of Math Object: 
Theorem
Major Section: 
Reference

Mathematics Subject Classification

15A60 no label found55-XX no label found46E30 no label found42B10 no label found42B05 no label found

Comments

perhaps
if $p$ and $q$ are such that $1/p+1/q=1$ then...

cause it looks like you're multiplying the norms with the fractions...
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

The H\"older inequality applies generally to objects in Banach spaces (also infinite dimensional) $L_p(X)$ and $L_q(X)$ (where, as always, $\frac{1}{p}+\frac{1}{q}=1$); it states that the product is integrable (a member of $L_1(X)$), and that the norms behave as required.

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