Riesz meets Sobolev

DOI10.4064/cm118-2-20zbMath1194.58027arXiv0911.2313OpenAlexW2054079314MaRDI QIDQ5306778

Thierry Coulhon, Adam S. Sikora

Publication date: 9 April 2010

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.2313

zbMATH Keywords

Riemannian manifoldheat kernelRiesz transformSobolev type inequality

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (11)

Gaussian heat kernel bounds through elliptic Moser iteration ⋮ Lie group approach to Grushin operators ⋮ Removable sets and \(L^p\)-uniqueness on manifolds and metric measure spaces ⋮ Well posedness and regularity for heat equation with the initial condition in weighted Orlicz-Slobodetskii space subordinated to Orlicz space like \(\lambda (\log\lambda )^\alpha\) and the logarithmic weight ⋮ Sobolev algebras through heat kernel estimates ⋮ Gaussian heat kernel estimates: from functions to forms ⋮ Riesz transforms for bounded Laplacians on graphs ⋮ Gradient estimates for heat kernels and harmonic functions ⋮ Estimates for operators related to the sub-Laplacian with drift in Heisenberg groups ⋮ Riesz transforms on a class of non-doubling manifolds ⋮ On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces

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