  This work studies the Hardy number for the class of hyperbolic planar domains
satisfying Abel's inclusion property, which are usually known as Koenigs
domains. More explicitly, we prove that for all regular domains in the above
class, the Hardy number is greater or equal than $1/2$, and this lower bound is
sharp. In contrast to this result, we provide examples of general domains whose
Hardy numbers are arbitrarily small. Additionally, we outline the connection of
the aforementioned class of domains with the discrete dynamics of the unit disc
and obtain results on the range of Hardy number of Koenigs maps, in the
hyperbolic and parabolic case.
