Riesz transform and related inequalities on non‐compact Riemannian manifolds
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Publication:4434570
DOI10.1002/cpa.3040zbMath1037.58017OpenAlexW2128690619WikidataQ115406252 ScholiaQ115406252MaRDI QIDQ4434570
Thierry Coulhon, Xuan Thinh Duong
Publication date: 10 November 2003
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.3040
Special integral transforms (Legendre, Hilbert, etc.) (44A15) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Kernel operators (47B34)
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Cites Work
- Unnamed Item
- Riesz transform, Gaussian bounds and the method of wave equation
- Isometric Riemannian manifolds at infinity
- Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
- Riesz transforms for
- An Application of Homogenization Theory to Harmonic Analysis: Harnack Inequalities And Riesz Transforms on Lie Groups of Polynomial Growth
- Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
- Fractional powers of operators