Heat kernel estimates of fractional Schrödinger operators with negative Hardy potential

DOI10.1007/s11118-019-09795-7zbMath1459.60153arXiv1809.02425OpenAlexW2967584827MaRDI QIDQ2196595

Jian Wang, Tomasz Jakubowski

Publication date: 3 September 2020

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.02425

zbMATH Keywords

heat kernelfractional LaplacianHardy potentialDuhamel's formulathe Chapman-Kolmogorov equationthe Feynman-Kac formula

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Transition functions, generators and resolvents (60J35) Fractional partial differential equations (35R11) Jump processes on general state spaces (60J76)

Related Items

Heat kernel of fractional Laplacian with Hardy drift via desingularizing weights, Generalized Hardy operators, Hardy spaces associated to generalized Hardy operators and applications, Heat kernel estimates for subordinate Markov processes and their applications, Fractional Kolmogorov operator and desingularizing weights, Poisson problems involving fractional Hardy operators and measures, Ground-state representation for fractional Laplacian on half-line, Relativistic stable operators with critical potentials, Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings, Variation and oscillation operators associated to semigroup generated by Schrödinger operator with fractional power, Unnamed Item, On scales of Sobolev spaces associated to generalized Hardy operators, Decay of harmonic functions for discrete time Feynman--Kac operators with confining potentials, Optimal Hardy inequality for the fractional Laplacian on \(L^p\), Schrödinger perturbations with concave control function

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hardy inequalities and non-explosion results for semigroups
• The effect of the Hardy potential in some Calderón-Zygmund properties for the fractional Laplacian
• Optimal results for the fractional heat equation involving the Hardy potential
• Estimates of the Green function for the fractional Laplacian perturbed by gradient
• Dirichlet forms and symmetric Markov processes.
• General analytic characterization of gaugeability for Feynman-Kac functionals
• Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
• Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes
• Stable estimates for source solution of critical fractal Burgers equation
• Heat kernel estimates for the Dirichlet fractional Laplacian
• Estimates of integral kernels for semigroups associated with second-order elliptic operators with singular coefficients
• Global heat kernel bounds via desingularizing weights
• Estimates of perturbation series for kernels
• Gradient estimates of \(q\)-harmonic functions of fractional Schrödinger operator
• On combinatorics of Schrödinger perturbations
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
• The Heat Equation with a Singular Potential
• Time-dependent Schrödinger perturbations of transition densities
• Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation
• The heat kernel of a Schrödinger operator with inverse square potential
• Gaugeability for Feynman-Kac functionals with applications to symmetric 𝛼-stable processes
• A convolution equation and hitting probabilities of single points for processes with stationary independent increments
• Fractional Laplacian with Hardy potential
• Bernstein functions. Theory and applications