On Bilinear Hardy Inequality and Corresponding Geometric Mean Inequality

Amiran Gogatishvili; Pankaj Jain; Saikat Kanjilal

arXiv:2009.05546·math.FA·July 20, 2022

On Bilinear Hardy Inequality and Corresponding Geometric Mean Inequality

Amiran Gogatishvili, Pankaj Jain, Saikat Kanjilal

PDF

TL;DR

This paper establishes multiple equivalent conditions for bilinear Hardy inequalities within certain parameter ranges, enhancing understanding of their structure and applications.

Contribution

It introduces several scales of equivalent conditions for bilinear Hardy inequalities when q is greater than or equal to the maximum of p1 and p2.

Findings

01

Derived multiple equivalent conditions for the inequalities

02

Extended the understanding of bilinear Hardy inequalities

03

Provided tools for further analysis of related inequalities

Abstract

The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case $1 < q, p_{1}, p_{2} < \infty$ with $q \geq max (p_{1}, p_{2})$ .

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.