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On the H.-Q. Li inequality on step-two Carnot groups
Ye Zhang1
1 Analysis on Metric Spaces Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1107-1114.

In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q. Li inequality. As a byproduct, we provide a simpler proof of the fact that the constant in H.-Q. Li inequality is strictly larger than 1.

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DOI : 10.5802/crmath.475
Classification : 58J35, 22E30, 35H10, 35R03
Ye Zhang 1

1 Analysis on Metric Spaces Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Ye Zhang. On the H.-Q. Li inequality on step-two Carnot groups. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1107-1114. doi : 10.5802/crmath.475. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.475/

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