Integral operators, embedding theorems, Taylor coefficients, isometries, boundary behaviour of Area-Nevanlinna type spaces in higher dimension and related problems

Abstract

This paper contains an overview of recent results of Area-Nevanlinna classes in higher dimension. We here consider various aspects of this new interesting research area of analytic function theory in higher dimension (integral operations, embedding theorems, Taylor coefficients). Previously in one dimension all these results were known. New open interesting Problems in this new research area will be also discussed and indicated.

Keywords

• polydisk
• unit ball
• taylor coefficients
• integral operators
• analytic functions
• analytic spaces
• area nevanlinna type spaces
• tubular domain
• pseudoconvex domain
• isometries
• boundary behaviour
• полидиск
• шар
• классы типа неванлинны
• аналитические функции
• теоремы вложения
• коэффициенты тэйлора
• изометрии
• интегральные операторы
• характеристика типа неванлинны
• трубчатые и псевдовыпуклые области