Gradient estimates for heat kernels and harmonic functions

DOI10.1016/j.jfa.2019.108398zbMath1439.53041arXiv1703.02152OpenAlexW2991083297WikidataQ109744473 ScholiaQ109744473MaRDI QIDQ2291609

Adam S. Sikora, Pekka Koskela, Thierry Coulhon, Ren Jin Jiang

Publication date: 31 January 2020

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.02152

zbMATH Keywords

harmonic functionheat kernelDirichlet formRiesz transformmetric measure spaceLi-Yau estimate

Mathematics Subject Classification ID

Dirichlet forms (31C25) Harmonic analysis on homogeneous spaces (43A85) Elliptic equations on manifolds, general theory (58J05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Potential theory on fractals and metric spaces (31E05) Heat kernel (35K08)

Related Items (19)

Gradient estimates for Schrödinger operators with characterizations of 𝐵𝑀𝑂_{ℒ} on Heisenberg groups ⋮ NOTES ON CONFORMAL PERTURBATION OF HEAT KERNELS ⋮ Dirichlet problem for Schrödinger equation with the boundary value in the BMO space ⋮ Volume growth on manifolds with quadratic curvature decay and its applications ⋮ Removable singularity of positive mass theorem with continuous metrics ⋮ On the caloric functions with BMO traces and their limiting behaviors ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ Poincaré constant on manifolds with ends ⋮ Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds ⋮ Systems of dyadic cubes of complete, doubling, uniformly perfect metric spaces without detours ⋮ Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces ⋮ Riesz transform via heat kernel and harmonic functions on non-compact manifolds ⋮ On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds ⋮ On gradient estimates for heat kernels ⋮ Riesz transform under perturbations via heat kernel regularity ⋮ Estimates for operators related to the sub-Laplacian with drift in Heisenberg groups ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

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