Finite Sections of Weighted Carleman's Inequality

TL;DR

This paper investigates finite segments of weighted Carleman's inequality, deriving asymptotic expressions for the best possible constants using De Bruijn's approach.

Contribution

It extends the analysis of Carleman's inequality to weighted finite sections, providing new asymptotic results for the optimal constants.

Findings

Derived asymptotic expressions for optimal constants in weighted Carleman's inequality

Extended De Bruijn's approach to weighted finite sections

Provided insights into the behavior of inequalities in finite settings

Abstract

We study finite sections of weighted Carleman's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.