Estimates of heat kernels for non-local regular Dirichlet forms

DOI10.1090/S0002-9947-2014-06034-0zbMath1304.47058OpenAlexW2061155316MaRDI QIDQ2930654

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

Publication date: 19 November 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2014-06034-0

zbMATH Keywords

heat kernelheat semigroupeffective resistancenon-local Dirichlet form

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Fractals (28A80) Transition functions, generators and resolvents (60J35)

Related Items

Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces, Heat kernel estimates for non-symmetric finite range jump processes, 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, Random walks and induced Dirichlet forms on self-similar sets, Upper heat kernel estimates for nonlocal operators via Aronson's method, Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, Davies’ method for anomalous diffusions, ``The Sierpinski gasket minus its bottom line as a tree of Sierpinski gaskets, Markov chain approximations for nonsymmetric processes, Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces, Characterizations of heat kernel estimates for symmetric non-local Dirichlet forms via resistance forms, Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces, On the conservativeness of some Markov processes, Heat kernel estimates for symmetric jump processes with mixed polynomial growths, The Davies method revisited for heat kernel upper bounds of regular Dirichlet forms on metric measure spaces, Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders, Stability of heat kernel estimates for symmetric non-local Dirichlet forms, Escape rate of symmetric jump-diffusion processes, Regularity estimates for elliptic nonlocal operators, Semipolar sets and intrinsic Hausdorff measure, Local and non-local Dirichlet forms on the Sierpiński carpet, Heat kernel estimates for anomalous heavy-tailed random walks, Analysis and stochastic processes on metric measure spaces, Heat kernels and non-local Dirichlet forms on ultrametric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On stochastic completeness of jump processes
• Dirichlet forms and symmetric Markov processes.
• Comparison inequalities for heat semigroups and heat kernels on metric measure spaces
• Conservation property of symmetric jump processes
• Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces
• Generalized Bessel and Riesz potentials on metric measure spaces
• On the parabolic kernel of the Schrödinger operator
• Upper bounds for symmetric Markov transition functions
• Analysis on Wiener spaces. II: Differential forms
• Estimates of transition densities for Brownian motion of nested fractals
• Harmonic analysis for resistance forms.
• Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
• Heat kernel estimates for jump processes of mixed types on metric measure spaces
• Heat kernel estimates for stable-like processes on \(d\)-sets.
• Transition Probabilities for Symmetric Jump Processes
• Domains of Dirichlet forms and effective resistance estimates on p.c.f. fractals
• NASH-TYPE INEQUALITIES AND HEAT KERNELS FOR NON-LOCAL DIRICHLET FORMS
• Heat kernel upper bounds for jump processes and the first exit time
• Non-local Dirichlet forms and symmetric jump processes
• Volume doubling measures and heat kernel estimates on self-similar sets
• Brownian motion on nested fractals
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Heat kernels on metric measure spaces and an application to semilinear elliptic equations
• AN ANALYTICAL APPROACH TO HEAT KERNEL ESTIMATES ON STRONGLY RECURRENT METRIC SPACES
• Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs