Duality of Lp spaces
= Duality of Lp spaces
{title2=$(L^p)^*=L^q$}
For $1\leq p<\infty$ and conjugate exponent $q$, every bounded linear functional on $L^p$ over a sigma-finite measure space has the form
$$
f\longmapsto\int f\omega
$$
for a unique $\omega\in L^q$, and its operator norm is $\|\omega\|_q$. At the endpoint $p=1$, this says $(L^1)^*=L^\infty$.
This identifies the <continuous dual space> of an <Lp space>; it is not an alternative definition of the entire Lp-space topic.