# Intrinsic operators from holomorphic function spaces to growth spaces

## TL;DR

This paper characterizes when certain operators from Banach spaces of holomorphic functions to growth spaces are bounded or compact, showing these properties depend only on point evaluation behavior and generalizing previous results.

## Contribution

It provides a unified framework for understanding the boundedness and compactness of a broad class of intrinsic operators, extending known results to more general settings.

## Key findings

- Boundedness and compactness depend solely on point evaluation behavior.
- Generalization of results for multiplication, composition, and integral operators.
- Applicable to a wide class of Banach spaces of holomorphic functions.

## Abstract

We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth of the functions derivatives. The results show that the boundedness and compactness of such intrinsic operators depends only on the behaviour on the point evaluation functionals. They also generalize previous similar results about several specific classes of operators, such as the multiplication, composition and integral operators.