Area Nevanlinna Type Classes of Analytic Functions in the Unit Disk and Related Spaces

Abstract

The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concerning zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.

Интегральные Операторы, Теоремы Вложения, Изометрии, Граничное Поведение И Коэффициенты Тэйлора Многомерных Пространств Типа Неванлинны И Связанные С Ними Проблемы

“…Even in particular cases of unit ball and polydisk a lot of open problems in this area related with both these problems in area Nevanlinna type spaces. Note if p ≥ 1, then (log + | f (z)|) p is subharmonic and this fact is some cases is crucial for proofs of such type embeddings (see, for example, [1,17,18,19]).…”

“…This paper is the second part of our notes on area Nevanlinna type spaces. We refer to [1] for the first part related with spaces of this type in one variable. Known various one dimensional results related with such spaces will not be included in this paper.…”