Generalization of the Boundary Uniqueness Theorem for A(z)—Analytic Functions

We consider A(z)—analytic functions in case when A(z) is antianalytic function. In this paper, the Nevanlinna class for A(z)—analytic functions is are introduced and for these classes, the boundary values of the function are investigated. For the Nevanlinna class of functions, an analogue of Fatou’s theorem was proved as a proposition to show that the function has a value on the boundary of the domain. Also, the Privalov’s ice-cream cone consruction is introduced for A(z)—analytic functions and Egoroff’s theorems are applied for them. As the main result, the analog generalized boundary uniqueness theorem for A(z)—analytic functions is proven and the boundary uniqueness theorem for Nevanlinna classes of functions are given as a corollary.