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Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
About this Title
Donatella Danielli, Nicola Garofalo and Duy-Minh Nhieu
Publication: Memoirs of the American Mathematical Society
Publication Year:
2006; Volume 182, Number 857
ISBNs: 978-0-8218-3911-9 (print); 978-1-4704-0461-1 (online)
DOI: https://doi.org/10.1090/memo/0857
MathSciNet review: 2229731
MSC: Primary 43A85; Secondary 35H20, 46E35
Table of Contents
Chapters
- 1. Introduction
- 2. Carnot groups
- 3. The characteristic set
- 4. $X$-variation, $X$-perimeter and surface measure
- 5. Geometric estimates from above on CC balls for the perimeter measure
- 6. Geometric estimates from below on CC balls for the perimeter measure
- 7. Fine differentiability properties of Sobolev functions
- 8. Embedding a Sobolev space into a Besov space with respect to an upper Ahlfors measure
- 9. The extension theorem for a Besov space with respect to a lower Ahlfors measure
- 10. Traces on the boundary of $(\epsilon , \delta )$ domains
- 11. The embedding of $B^p_\beta (\Omega , d\mu )$ into $L^q(\Omega , d\mu )$
- 12. Returning to Carnot groups
- 13. The Neumann problem
- 14. The case of Lipschitz vector fields