Abstract:

The central concept of R. Nevanlinna's theory of meromorphic functions is the concept of characteristic function.  In complex analysis, classes of functions of bounded type and Nevanlinna-Dzhrbashyan classes, introduced in R. Nevanlinna's monograph, are well known. These classes and their analytic subclasses played an important role in the development of the theory of functions of a complex variable. In 1964, M. Dzhrbashyan attempted to generalize R. Nevanlinna's harmonious theory by introducing a new characteristic function and classes of meromorphic functions with bounded $\alpha$-characteristic. It turned out that the introduced classes are wider than the Nevanlinna-Dzhrbashyan classes. Developing Nevanlinna's theory, F.A. Shamoyan in 1999 introduced and studied classes of meromorphic functions with R. Nevanlinna characteristic from $L^p$-weighted spaces. The connection between Shamoyan's classes and Dzhrbashyan's weight classes is studied in this paper.