Heat kernels and Riesz transforms on nilpotent Lie groups

Research Report MRR96-056

Heat kernels and Riesz transforms on nilpotent Lie groups

A.F.M. ter Elst, Derek W. Robinson and Adam Sikora

Abstract: We consider pure m-th 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

-spaces with $p\in\langle1,\infty\rangle$ . Finally for second-order operators with real coefficients we derive matching Gaussian lower bounds and deduce Harnack inequalities valid for all times.

AMS Subject Classification: 35J30, 22E25, 44A15.

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