TY - JOUR
T1 - Heat kernel estimates and Riesz transforms on some Riemannian covering manifolds
AU - Dungey, Nick
PY - 2004/8
Y1 - 2004/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=3543022702&partnerID=8YFLogxK
U2 - 10.1007/s00209-003-0646-4
DO - 10.1007/s00209-003-0646-4
M3 - Article
SN - 0025-5874
VL - 247
SP - 765
EP - 794
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 4
ER -