From integral estimates of functions to uniformly and locally averaged

TL;DR

This paper introduces a new approach using integral Jensen's inequality with convex functions to derive pointwise estimates from integral restrictions on functions, advancing the understanding of function growth behavior.

Contribution

It presents a novel method leveraging integral Jensen's inequality to obtain pointwise estimates from integral growth conditions in function theory.

Findings

Provides a new technique for pointwise estimates

Connects integral restrictions with local function behavior

Enhances tools for analyzing function growth

Abstract

Problems pointwise estimates from above functions or its averages often arise in the function theory under known integral restrictions on the growth of this function. We offer an approach to such problems based on the integral Jensen's inequality with the convex function