The boundary behavior of holomorphic functions: global and local results (Q2472599)

Using two new localized maximal functions, the author develops some new techniques for studying the boundary limiting behavior of a holomorphic function on a domain both in one and several complex variables. As a result, new proofs of Caldéron type theorems on the local boundary behavior on a set of positive measure may be obtained. There is also studied connection between the property of nontangential boundedness (on a set of positive measure) and admissible boundedness. Under suitable hypotheses, these two conditions are shown to be equivalent.