Dual of p-integrable functions

Question

Consider a Banach space $X$ and a $\sigma$-finite measurable space $(\Omega,\mathcal{A},\mu)$. The space of $p$-integrable functions is defined by $L^p(\Omega,X):=\{ f:\Omega\to X\text{ measurable} : \int_\Omega \|f(\omega)\|^p d\mu <\infty\}$. I'm looking for a reference about the dual space of this space, I've found mentions in some works that the dual is $L^q(\Omega,X^\ast)$ where $X^\ast$ is endowed by the weak$^\ast$ topology and $1/p+1/q = 1$, but I can't find an article or book that provides that result. If you know about any reference of it, I will be very grateful if you can give me. Thanks in advance!