Non-tangential maximal moduli and harmonic functions on the upper half plane (part 1)

Abstract

In this paper, we present some nice theorems on non-tangential maximal moduli associated to real-valued harmonic functions on the upper half plane. Some necessary and sufficient conditions using nontangential moduli to characterize real parts of holomorphic functions with their boundary value functions having smoothness of high order will be presented in this paper and the second paper.