Finite Sections of Weighted Hardy's Inequality

TL;DR

This paper investigates finite segments of weighted Hardy's inequality, deriving an asymptotic formula for the best constant using De Bruijn's approach, extending known results from the unweighted case.

Contribution

It provides a new asymptotic expression for the optimal constant in finite sections of weighted Hardy's inequality, advancing understanding of weighted inequalities.

Findings

Derived asymptotic expression for the optimal constant

Extended unweighted Hardy's inequality results to weighted case

Used De Bruijn's approach for analysis

Abstract

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