Reference : Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannia...
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/47902
Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannian manifolds
English
Cao, Jun [Zhejiang University of Technology > Department of Applied Mathematics]
Cheng, Li-Juan [Zhejiang University of Technology > Department of Applied Mathematics]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
30-Aug-2021
34
No
[en] We address some fundamental questions concerning geometric analysis on Riemannian manifolds. It has been asked whether the Lp-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 1 < p < 2 under the natural assumption of a lower bound on the Ricci curvature. For p > 2, 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.
Researchers ; Professionals
http://hdl.handle.net/10993/47902
https://math.uni.lu/thalmaier/PREPRINTS/CZ.html
https://arxiv.org/abs/2108.13058

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