Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannian manifolds
by Jun Cao, Li-Juan Cheng and Anton Thalmaier
Abstract
We address some fundamental questions
concerning geometric analysis on Riemannian manifolds. It has been
asked whether the -Calderón-Zygmund
inequalities extend to
a reasonable class of non-compact Riemannian manifolds without the
assumption of a positive injectivity radius. In the present
paper, we give a positive answer for under the natural
assumption of a lower bound on the Ricci curvature.
For , we complement the study in
Güneysu-Pigola (2015) and derive sufficient geometric criteria
for the validity of the Calderón-Zygmund inequality by adding
Kato class bounds on the Riemann curvature tensor and the covariant
derivative of Ricci curvature. Probabilistic tools, like Hessian
formulas and Bismut type representations for heat semigroups, play
a significant role throughout the proofs.
The paper is available here:
Back to Homepage