Differential-free characterisation of smooth mappings with controlled growth

TL;DR

This paper generalizes and improves a characterization of the Bloch space of smooth functions in the unit ball, focusing on differential-free methods and controlled growth conditions.

Contribution

It introduces new generalizations and enhancements to existing characterizations of the Bloch space without relying on derivatives, emphasizing growth control.

Findings

Extended the Holland-Walsh characterization to broader classes of functions.

Provided differential-free criteria for smooth mappings with controlled growth.

Improved understanding of the structure of the Bloch space in higher dimensions.

Abstract

In this paper we give some generalizations and improvements of the Pavlovi\'c result on the Holland-Walsh type characterization of the Bloch space of continuously differentiable (smooth) functions in the unit ball in $\mathbf{R}^m$.