TL;DR
This paper introduces trace conjunction integrals and inequalities that unify classical inequalities like Hardy and Gagliardo trace, revealing new endpoint formulas and open problems in analysis.
Contribution
It defines trace conjunction integrals and inequalities, unifying key classical inequalities and establishing endpoint formulas with open questions.
Findings
Unified Hardy and Gagliardo trace inequalities
Established Bourgain-Brezis-Mironescu formula at endpoints
Identified new open problems in trace analysis
Abstract
Trace conjunction integrals are introduced and studied. They appear in trace conjunction inequalities which unify the Hardy inequality on a halfspace and the classical Gagliardo trace inequality. At the endpoint they satisfy a Bourgain-Brezis-Mironescu formula for smooth maps, which raises some new open problems.
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.