"Volume 155, number 739 (end of volume)."

Includes bibliographical references (p. 99-101).

1. Introduction and statement of the results 2. The control distance and the local Harnack inequality 3. The proof of the Harnack inequality from Varopoulos's theorem and Propositions 1.6.3 and 1.6.4 4. H�older continuity 5. Nilpotent Lie groups 6. Sub-Laplacians on nilpotent Lie groups 7. A function which grows linearly 8. Proof of Propositions 1.6.3 and 1.6.4 in the case of nilpotent Lie groups 9. Proof of the Gaussian estimate in the case of nilpotent Lie groups 10. Polynomials on nilpotent Lie groups 11. A Taylor formula for the heat functions on nilpotent Lie groups 12. Harnack inequalities for the derivatives of the heat functions on nilpotent Lie groups 13. Harmonic functions of polynomial growth on nilpotent Lie groups 14. Proof of the Berry-Esseen estimate in the case of nilpotent Lie groups 15. The nil-shadow of a simply connected solvable Lie group 16. Connected Lie groups of polynomial volume growth 17. Proof of Propositions 1.6.3 and 1.6.4 in the general case 18. Proof of the Gaussian estimate in the general case 19. A Berry-Esseen estimate for the heat kernels on connected Lie groups of polynomial volume growth 20. Polynomials on connected Lie groups of polynomial growth 21. A Taylor formula for the heat functions on connected Lie groups of polynomial volume growth 22. Harnack inequalities for the derivatives of the heat functions 23. Harmonic functions of polynomial growth 24. Berry-Esseen type of estimates for the derivatives of the heat kernel 25. Riesz transforms

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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