  The article is devoted to the study of mappings that distort the modulus of
families of paths according to the Poletsky inequality type. At the boundary
points of the domain, we have obtained an estimate of the distance distortion
for such mappings provided that their characteristic has finite integral
averages over the balls, and the image domain of mappings is Ahlfors regular
and such that the Poincare inequality holds. The manuscript considers the cases
of homeomorphisms and mappings with branching, as well as definition domains
with good boundaries and domains with prime ends.
