Riesz transforms on connected sums

DOI10.5802/aif.2334zbMath1139.58020arXivmath/0602269OpenAlexW1587030255WikidataQ125789651 ScholiaQ125789651MaRDI QIDQ2477561

Gilles Carron

Publication date: 14 March 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602269

zbMATH Keywords

Riemannian manifoldSobolev inequalitiesRiesz transform

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (12)

Functional calculus of operators with heat kernel bounds on non-doubling manifolds with ends ⋮ Gundy-Varopoulos martingale transforms and their projection operators on manifolds and vector bundles ⋮ Vertical and horizontal square functions on a class of non-doubling manifolds ⋮ BMO spaces associated to operators with generalised Poisson bounds on non-doubling manifolds with ends ⋮ A Gaussian estimate for the heat kernel on differential forms and application to the Riesz transform ⋮ Riesz transform via heat kernel and harmonic functions on non-compact manifolds ⋮ The Hodge-de Rham Laplacian and \(L^p\)-boundedness of Riesz transforms on non-compact manifolds ⋮ Gaussian heat kernel estimates: from functions to forms ⋮ Riesz transform under perturbations via heat kernel regularity ⋮ Riesz transforms for bounded Laplacians on graphs ⋮ Estimates for operators related to the sub-Laplacian with drift in Heisenberg groups ⋮ Riesz transforms on a class of non-doubling manifolds

Cites Work

• Riesz transform and perturbation
• Comparaison des champs de vecteurs et des puissances du Laplacien sur une variété Riemannienne à courbure non positive
• Hardy-Littlewood theory for semigroups
• The Riesz transformation on conical varieties
• Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces
• Heat kernel upper bounds on a complete non-compact manifold
• Heat kernel on connected sums of Riemannian manifolds
• Stability results for Harnack inequalities.
• An exact sequence in \(L^2\)-cohomology
• Riesz transform and \(L^p\)-cohomology for manifolds with Euclidean ends
• An Application of Homogenization Theory to Harmonic Analysis: Harnack Inequalities And Riesz Transforms on Lie Groups of Polynomial Growth
• Riesz transforms for $1\le p\le 2$
• Riesz transform and related inequalities on non‐compact Riemannian manifolds
• Optimal Sobolev Inequalities on Complete Riemannian Manifolds with Ricci Curvature Bounded Below and Positive Injectivity Radius
• Fractional powers of operators
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