Gradient estimates for heat kernels and harmonic functions

2017/03/06 by Coulhon, Thierry, Jiang, Renjin, Koskela, Pekka +1 · 2 citations
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1703.02152

Abstract

Let (X,d,μ) be a doubling metric measure space endowed with a Dirichlet form \E deriving from a "carré du champ". Assume that (X,d,μ,\E) supports a scale-invariant L²-Poincaré inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for p∈ (2,∞]: (i) (G_p): L^p-estimate for the gradient of the associated heat semigroup; (ii) (RH_p): L^p-reverse Hölder inequality for the gradients of harmonic functions; (iii) (R_p): L^p-boundedness of the Riesz transform (p

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• On the Reverse Inequality of Riesz transform on metric cone with potential
• On the Interplay Between Hodge Projections and Bounded Harmonic Functions on Manifolds with Ends

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