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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

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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 Varopoulos's theorem and Propositions 1.6.3 and 1.6.4
  • 4. Hölder 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