Comparison inequalities for heat semigroups and heat kernels on metric measure spaces

DOI10.1016/j.jfa.2010.07.010zbMath1207.58021OpenAlexW2067586240MaRDI QIDQ709224

Jiaxin Hu, Alexander Grigor'yan, Ka-Sing Lau

Publication date: 18 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2010.07.010

zbMATH Keywords

maximum principleheat kernelDirichlet formheat semigroup

Mathematics Subject Classification ID

Dirichlet forms (31C25) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Groups and semigroups of linear operators, their generalizations and applications (47D99) Analysis on metric spaces (30L99)

Related Items (17)

Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces ⋮ Two-sided estimates of heat kernels of jump type Dirichlet forms ⋮ The Davies method for heat kernel upper bounds of non-local Dirichlet forms on ultra-metric spaces ⋮ A geometric interpretation of the transition density of a symmetric Lévy process ⋮ Estimates of heat kernels for non-local regular Dirichlet forms ⋮ Upper estimates of transition densities for stable-dominated semigroups ⋮ Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces ⋮ Two-sided estimates of heat kernels on metric measure spaces ⋮ On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals ⋮ Heat kernel asymptotics for the measurable Riemannian structure on the Sierpinski gasket ⋮ Initial value problem and the heat kernel for a mixed type operator ⋮ Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces ⋮ Log-periodic asymptotic expansion of the spectral partition function for self-similar sets ⋮ Stability of heat kernel estimates for symmetric non-local Dirichlet forms ⋮ Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula ⋮ Local and non-local Dirichlet forms on the Sierpiński carpet ⋮ Heat kernels and non-local Dirichlet forms on ultrametric spaces

Cites Work

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• Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces
• Heat kernel on manifolds with ends
• On the parabolic kernel of the Schrödinger operator
• Brownian motion on the Sierpinski gasket
• Dirichlet forms and symmetric Markov processes
• Volume doubling measures and heat kernel estimates on self-similar sets
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Local Nash Inequality and Inhomogeneity of Heat Kernels
• On the relation between elliptic and parabolic Harnack inequalities

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