# H\"older inequality

## Primary tabs

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

## Mathematics Subject Classification

### layout?

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

### More that just "vector" p-norms

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.