A Reverse Hilbert-like Optimal Inequality

TL;DR

This paper introduces a new inequality for positive real numbers, resembling a reverse Hilbert inequality, and demonstrates its optimality using Fourier analysis techniques.

Contribution

It presents a novel reverse inequality related to Hilbert's inequality and proves its optimality with innovative Fourier analysis methods.

Findings

Established a new reverse Hilbert-like inequality.

Proved the inequality's optimality.

Used Fourier analysis in a novel way.

Abstract

We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.