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ArticleOriginal scientific text

Title

Heat kernels and Riesz transforms on nilpotent Lie groups

Authors 1, 2, 2

Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
  2. Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia

Abstract

We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian lower bounds and deduce Harnack inequalities valid for all times.

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Colloquium Mathematicum
1997/74/2
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Pages:
191-218
Main language of publication
English
Received
1996-12-03
Published
1998
Exact and natural sciences