  We develop a new technique for studying the boundary limiting behavior of a
holomorphic function on a domain $\Omega$ -- both in one and several complex
variables. The approach involves two new localized maximal functions. As a
result of this methodology, theorems of Calder\'{o}n type about local boundary
behavior on a set of positive measure may be proved in a new and more natural
way. We also study the question of nontangential boundedness (on a set of
positive measure) versus admissible boundedness. Under suitable hypotheses,
these two conditions are shown to be equivalent.
