Nevanlinna counting function and Carleson function of analytic maps

TL;DR

This paper proves that the maximal Nevanlinna counting function and the Carleson function for analytic self-maps of the unit disk are equivalent within constant factors, establishing a fundamental relationship between these two functions.

Contribution

It demonstrates the equivalence of the Nevanlinna counting function and the Carleson function for analytic self-maps, clarifying their relationship in complex analysis.

Findings

Maximal Nevanlinna counting function and Carleson function are equivalent up to constants.

Establishes a fundamental link between two key functions in complex analysis.

Provides a basis for further analysis of analytic self-maps of the disk.

Abstract

We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants.