0000000001043979
AUTHOR
Thierry Coulhon
Gradient estimates for heat kernels and harmonic functions
Let $(X,d,\mu)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carr\'e du champ". Assume that $(X,d,\mu,\E)$ supports a scale-invariant $L^2$-Poincar\'e inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\in (2,\infty]$: (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat semigroup; (ii) $(RH_p)$: $L^p$-reverse H\"older inequality for the gradients of harmonic functions; (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\infty$); (iv) $(GBE)$: a generalised Bakry-\'Emery condition. We show that, for $p\in (2,\infty)$, (i), (ii) (iii) are equivalent, wh…
Comité d'évaluation HCERES Unité BAGAP -Biodiversity, agroecology and landscape management under the supervision of the following Institutions and research bodies: Institut national de recherche pour l'agriculture, l'alimentation et l'environnement -INRAE Institut Agro -Agrocampus Ouest -École nationale des sciences agronomiques, agroalimentaires, horticoles et du paysage Groupe ESA -École Supérieure d'Agricultures Angers Loire EVALUATION CAMPAIGN 2020-2021 GROUP B
Under the decree No.2014-1365 dated 14 November 2014, 1 The president of Hcéres "countersigns the evaluation reports set up by the experts committees and signed by their chairman." (Article 8, paragraph 5); 2 The evaluation reports "are signed by the chairman of the experts committee". (Article 11, paragraph 2).