TL;DR
This paper explores a weighted form of Carleman's inequality using classical methods and applies the findings to prove a conjecture posed by Bennett.
Contribution
It introduces a weighted version of Carleman's inequality and confirms Bennett's conjecture through this new approach.
Findings
Established a weighted Carleman's inequality
Proved Bennett's conjecture using the new inequality
Enhanced understanding of inequality weights
Abstract
We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematics and Applications · Mathematical Inequalities and Applications