In what Sobolev classes are the following functions

Question

I need a little help. In what Sobolev classes are the following (give the answer for both $H^{s}$ and $H_{\mathrm{loc}}^{s}$)

a. $\delta(x)$

b. $H(x)=\left\{\begin{matrix} 1, x\geq 0\\ 0, x<0 \end{matrix}\right.$

c. The characteristic function of the unit disc in $\mathbb{R}^{2}$.

d. $1/x$ on $\mathbb{R}$ (defined by principal values)

e. the distribution obtained by integrating a function over the unit sphere.

Where $H_{\mathrm{loc}}^{s}(\mathbb{R}^{n})=\left \{ u:\phi u\in H^{s}(\mathbb{R}^{n}), \forall \phi \in C_{0}^{\infty}\right \}$.

Thanks a lot!