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Heat kernel estimates and Riesz transforms on some Riemannian covering manifolds

Dungey, Nicholas


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.

CollectionsANU Research Publications
Date published: 2004
Type: Journal article
Source: Mathematische Zeitschrift
DOI: 10.1007/s00209-003-0646-4


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