 Duality of Lp spaces

For $1\le p<\infty$ and conjugate exponent $q$, every bounded linear functional on $L^p$ over a sigma-finite measure space has the formfor a unique $\omega \in L^q$, and its operator norm is $\Vert \omega {\Vert }_q$. At the endpoint $p=1$, this says $(L^1{)}^{\ast }=L^{\infty }$.

This identifies the continuous dual space of an Lp space; it is not an alternative definition of the entire Lp-space topic.