# Sub-Laplacians with drift on Lie groups of polynomial volume growth

### About this Title

**Georgios K. Alexopoulos**

Publication: Memoirs of the American Mathematical Society

Publication Year
2002: Volume 155, Number 739

ISBNs: 978-0-8218-2764-2 (print); 978-1-4704-0332-4 (online)

DOI: http://dx.doi.org/10.1090/memo/0739

MathSciNet review: 1878341

MSC (2000): Primary 22E25; Secondary 22E30, 43A80

### Table of Contents

**Chapters**

- 1. Introduction and statement of the results
- 2. The control distance and the local Harnack inequality
- 3. The proof of the Harnack inequality from Varopoulosâ€™s theorem and Propositions 1.6.3 and 1.6.4
- 4. HĂ¶lder 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