On the H.-Q. Li inequality on step-two Carnot groups

Ye Zhang

doi:10.5802/crmath.475

Partial differential equations

On the H.-Q. Li inequality on step-two Carnot groups

Ye Zhang ¹

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.

Abstract

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 $1$ .

Received: 2022-11-16
Revised: 2023-02-03
Accepted: 2023-02-06
Published online: 2023-10-24

DOI: 10.5802/crmath.475

Classification: 58J35, 22E30, 35H10, 35R03

Author's affiliations:

Ye Zhang ¹

¹ Analysis on Metric Spaces Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {On the {H.-Q.} {Li} inequality on step-two {Carnot} groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1107--1114},
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     year = {2023},
     doi = {10.5802/crmath.475},
     language = {en},
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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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