From integral estimates of functions to uniform. I. Exact versions

TL;DR

This paper introduces a general method to derive sharp pointwise and uniform estimates of functions from their integral restrictions, with applications to Fock-Bargmann and Bergman spaces.

Contribution

It presents a novel scheme for obtaining precise function estimates from integral bounds, demonstrated through examples in complex analysis spaces.

Findings

Established a general method for sharp function estimates

Applied the method to Fock-Bargmann spaces

Applied the method to Bergman spaces in balls and polydiscs

Abstract

We give a general method to obtain from the integral restrictions of functions sharp pointwise and uniform estimates of these functions. This scheme is illustrated by the examples for Fock\,--\,Bargmann spaces of entire functions of several variables and Bergman spaces in balls and polydiscs.