Comparison of weight classes of analytical functions in a circle with restrictions on the Nevanlinna and Dzhrbashyan characteristics

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.