  In this paper we define Bessel potentials in Ahlfors regular spaces using a
Coifman type approximation of the identity, and show they improve regularity
for Lipschitz, Besov and Sobolev-type functions. We prove density and embedding
results for the Sobolev potential spaces defined by them. Finally, via
fractional derivatives, we find that for small orders, these Bessel potentials
are inversible, and show a way to characterize potential spaces, using singular
integrals techniques, such as the $T1$ theorem. Moreover, this characterization
allows us to prove these spaces in fact coincide with the classical potential
Sobolev spaces in the Euclidean case.
