Weak type (1,1) boundedness of Riesz transform on positively curved manifolds

DOI10.1007/s11401-008-0049-2zbMath0787.47027OpenAlexW2013109948MaRDI QIDQ1192404

Jiecheng Chen

Publication date: 27 September 1992

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-008-0049-2

zbMATH Keywords

gradientheat kernelLaplacianheat-diffusion semigroupcomplete Riemannian manifoldsweak-\(L^ 1(M)\)

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Linear operators on function spaces (general) (47B38) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (6)

The Riesz transformation on conical varieties ⋮ Covariant Riesz transform on differential forms for \(1 < p \leq 2\) ⋮ The second-order gradient estimates for the V-heat kernel and its applications ⋮ Riesz transformations on a class of manifolds with conical singularities ⋮ Riesz transform via heat kernel and harmonic functions on non-compact manifolds ⋮ Boundary behavior of harmonic functions on manifolds

Cites Work

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• Degenerate parabolic equations
• New results on the Cauchy problem for parabolic systems and equations with strongly nonlinear sources
• On the Cauchy problem and initial traces for the evolution \(p\)-Laplacian equations with strongly nonlinear sources
• On the Cauchy Problem and Initial Traces for a Degenerate Parabolic Equation
• Hölder estimates for nonlinear degenerate parabolic sytems.
• Degenerate parabolic equations with initial data measures

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