Probabilistic Behavior of Harmonic Functions

Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This work explores several aspects of this relationship. It focuses on the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory. Harmonic analysis and probability have enjoyed a mutually beneficial relationship. This monograph explores several aspects of this relationship. The primary focus of the text is the nonangential maximal function and the area function of a harmonic function and their probablistic analogues in martingale theory.