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September 29, 2025Open Access

Geometric Hardy inequalities on the Heisenberg groups via convexity

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The application of Hardy inequalities in Heisenberg groups shows superharmonicity indicating broader implications for convex domains.

The study establishes $L^p$-Hardy inequalities with constants for domains in the Heisenberg group.
Results are derived using the Euclidean distance on non-convex domains, and alternative methods for evaluating harder cases.
Implementations include gauge quasi-norm related to horizontal Laplacian and Carnot-Carathéodory distance in bounded convex domains.
The findings contribute to understanding superharmonicity and provide an alternative proof of the $L^2$-Hardy inequality.

Barbatis et al. (2025) studied this question.

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September 29, 2025Open Access

View Full Paper

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Authors

The application of Hardy inequalities in Heisenberg groups shows superharmonicity indicating broader implications for convex domains.

The study establishes $L^p$-Hardy inequalities with constants for domains in the Heisenberg group.
Results are derived using the Euclidean distance on non-convex domains, and alternative methods for evaluating harder cases.
Implementations include gauge quasi-norm related to horizontal Laplacian and Carnot-Carathéodory distance in bounded convex domains.
The findings contribute to understanding superharmonicity and provide an alternative proof of the $L^2$-Hardy inequality.

Barbatis et al. (2025) studied this question.

View Full Paper

Ask AI

Bookmark