2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115569We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $Ω$ -- both in one and several complex variables. The approach involves two new localized maximal functions. As a result of this methodology, theorems of Calderón 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.Complex Variables32A40, 31A20text