Let $k\in \mathbb{N}$, and consider the negative order Sobolev space $W^{-k,p}$. Given $p>1$, a distribution $f$ is in $W^{-k,p}$ if and only if, by definition of the space, $$ f=\sum_{|\alpha|\leq k}D^\alpha f_\alpha $$ see this question. They also state that the associated norm is defined as $$\inf\left\{\sum_{|\alpha|\leq k}\|f_\alpha\|_{L^p(\Omega)}\right\}$$
Now from what I understand, $\delta'$, the derivative of the Dirac delta distribution is in $W^{-1,p}$ but I have trouble working out its associated norm ? Similarly what then should be the norm of the Heaviside Theta distribution ?