Heat kernel estimates and Riesz transforms on some Riemannian covering manifolds

Nick Dungey*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    Consider a Riemannian manifold M which is a Galois covering of a compact manifold, with nilpotent deck transformation group G. For the Laplace operator on M, we prove a precise estimate for the gradient of the heat kernel, and show that the Riesz transforms are bounded in LP(M), 1 < p < ∞. We also obtain estimates for discrete oscillations of the heat kernel, and boundedness of discrete Riesz transform operators, which are defined using the action of G on M.

    Original languageEnglish
    Pages (from-to)765-794
    Number of pages30
    JournalMathematische Zeitschrift
    Volume247
    Issue number4
    DOIs
    Publication statusPublished - Aug 2004

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