Riesz transform under perturbations via heat kernel regularity

DOI10.1016/j.matpur.2019.02.009zbMath1433.58023arXiv1808.01948OpenAlexW2887870883MaRDI QIDQ2281149

Fang-Hua Lin, Ren Jin Jiang

Publication date: 19 December 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.01948

zbMATH Keywords

harmonic functionsmetric perturbationRiesz transformheat kernels

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Heat equation (35K05) Elliptic equations on manifolds, general theory (58J05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items

NOTES ON CONFORMAL PERTURBATION OF HEAT KERNELS, Dirichlet problem for Schrödinger equation with the boundary value in the BMO space, Maximal \(L^1\) regularity for solutions to inhomogeneous incompressible Navier-Stokes equations, On the caloric functions with BMO traces and their limiting behaviors, Gaussian estimates for heat kernels of higher order Schrödinger operators with potentials in generalized Schechter classes, Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces, The weighted Kato square root problem of elliptic operators having a BMO anti-symmetric part

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces
• Uniformly elliptic operators on Riemannian manifolds
• Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds
• Riesz transform and perturbation
• Heat kernel on manifolds with ends
• On the parabolic kernel of the Schrödinger operator
• Homogenization of elliptic problems with \(L^p\) boundary data
• The Riesz transformation on conical varieties
• Dirichlet forms and symmetric Markov processes
• On correctors for linear elliptic homogenization in the presence of local defects: the case of advection-diffusion
• Heat kernel estimates and Riesz transforms on some Riemannian covering manifolds
• Bounds of Riesz transforms on \(L^p\) spaces for second order elliptic operators.
• Riesz transform via heat kernel and harmonic functions on non-compact manifolds
• Gradient estimates for heat kernels and harmonic functions
• The Li-Yau inequality and heat kernels on metric measure spaces
• Stability of the Cheng-Yau gradient estimate
• Riesz transforms on connected sums
• Riesz transform and \(L^p\)-cohomology for manifolds with Euclidean ends
• Riesz transform on manifolds and heat kernel regularity
• THE HEAT EQUATION ON NONCOMPACT RIEMANNIAN MANIFOLDS
• A perturbation result for the Riesz transform
• Volumes of Small Balls on Open Manifolds: Lower Bounds and Examples
• Compactness methods in the theory of homogenization
• The local regularity of solutions of degenerate elliptic equations
• L^p bounds on singular integrals in homogenization
• An Application of Homogenization Theory to Harmonic Analysis: Harnack Inequalities And Riesz Transforms on Lie Groups of Polynomial Growth
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
• Riesz transforms for $1\le p\le 2$
• On correctors for linear elliptic homogenization in the presence of local defects
• Sobolev Spaces on Metric Measure Spaces
• Analysis on Lie groups