In this chapter, we shall primarily be focused on studying Herz-based Sobolev spaces (of first generation) on boundaries of Ahlfors regular domains, along with their homogeneous versions. Here, the Calderón-Zygmund theory on Herz spaces Ap,q developed in Chapter 13 plays an important role, as it allows us to develop a functional analytic theory for the aforementioned scales of Sobolev spaces. The consideration of these scales opens the door for treating boundary value problems in which the boundary data, hence also the solution, exhibit additional regularity.