Stratified Lie Groups and Potential Theory for their Sub-Laplacians

Part I. Elements of Analysis of Stratified Groups

1. Stratified Groups and Sub-Laplacians

2. Abstract Lie Groups and Carnot Groups

3. Carnot Groups of Step Two

4. Examples of Carnot Groups

5. The Fundamental Solution for a Sub-Laplacian and Applications

Part II. Elements of Potential Theory for Sub-Laplacians

6. Abstract Harmonic Spaces

7. The L-harmonic Space

8. L-subharmonic Functions

9. Representation Theorems

10. Maximum Principle on Unbounded Domains

11. L-capacity, L-polar Sets and Applications

12. L-thinness and L-fine Topology

13. d-Hausdorff Measure and L-capacity

Part III. Further Topics on Carnot Groups

14. Some Remarks on Free Lie Algebras

15. More on the Campbell–Hausdorff Formula

16. Families of Diffeomorphic Sub-Laplacians

17. Lifting of Carnot Groups

18. Groups of Heisenberg Type

19. The Carathéodory–Chow–Rashevsky Theorem

20. Taylor Formula on Homogeneous Carnot Groups

DRM-restrictions

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Avainsanat: MATHEMATICS / General MAT000000