Reference request for a notion of $L^p$ norm of a one-form.

Question

I am looking for a definition of $L^p$ norm for 1-forms on $\mathbb{R}^n$, with $n\geq1$. The first idea that I had was to set $$ \left\Vert\omega_kdx^k\right\Vert_p:=\sum_{k=1}^n\left\Vert\omega_k\right\Vert_{L^p(\mathbb{R}^n)} $$ but I'm not sure about the well-behaviour of this definition when changing coordinates. Can you please point me out any reference dealing with this argument? Any help is very appreciated.