Heat kernels and Riesz transforms on nilpotent Lie groups

• Autorzy: A. F. M. ter Elst , Derek W. Robinson , Adam Sikora
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 74
• Numer: 2
• Strony: 191-218

Daty

wydano

1998

otrzymano

1996-12-03

Twórcy

autor

A. F. M. ter Elst

• Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

autor

Derek W. Robinson

• Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia

autor

Adam Sikora

• Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia

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