Riesz transform on manifolds and heat kernel regularity

Pascal Auscher*, Thierry Coulhon, Xuan Thinh Duong, Steve Hofmann

*Corresponding author for this work

    Research output: Contribution to journalReview article

    131 Citations (Scopus)

    Abstract

    One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is Lp bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain Lp estimate in the same interval of p's.

    Original languageEnglish
    Pages (from-to)911-957
    Number of pages47
    JournalAnnales Scientifiques de l'Ecole Normale Superieure
    Volume37
    Issue number6
    DOIs
    Publication statusPublished - Nov 2004

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