Double logarithmic inequality with a sharp constant in four space dimensions

TL;DR

This paper establishes a precise double logarithmic inequality with an optimal constant for radially symmetric functions in four-dimensional space, advancing understanding of functional inequalities in higher dimensions.

Contribution

The authors prove a sharp Log Log inequality with an almost sharp constant specifically for radially symmetric functions in four dimensions.

Findings

Established a sharp Log Log inequality in four dimensions

Identified the constant as nearly optimal

Focused on radially symmetric functions

Abstract

We prove a Log Log inequality with a sharp constant in four dimensions for radially symmetric functions. We also show that the constant in the Log estimate is almost sharp.