I am reading some preliminary material to develop a good background in order to study PDE and I came across the following fact
The dual space of $L^p$ is $L^q$ where $q$ is the Holder's Conjugate of $p$, so in other words $\frac{1}{p}+\frac{1}{q}=1$. Can someone please explain to me how to prove this fact or indicate where can I read something about this that is understandable from somehow who doesn't have much knowledge of functional analysis.
I know the definition of dual space and I was reading on wikipedia that there is a natural isomorphism from the space of linear functionals of $L^p$ to $L^q$, but I can't really reason on why so, and the intuition behind this.