# Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Carathéodory Spaces

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*Donatella Danielli; Nicola Garofalo; Duy-Minh Nhieu*

#### Table of Contents

# Table of Contents

## Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces

- Contents vii8 free
- Chapter 1. Introduction 112 free
- Chapter 2. Carnot groups 1526
- Chapter 3. The characteristic set 2334
- Chapter 4. X-variation, X-perimeter and surface measure 3344
- Chapter 5. Geometric estimates from above on CC balls for the perimeter measure 3748
- Chapter 6. Geometric estimates from below on CC balls for the perimeter measure 4152
- Chapter 7. Fine differentiability properties of Sobolev functions 5768
- Chapter 8. Embedding a Sobolev space into a Besov space with respect to an upper Ahlfors measure 6576
- Chapter 9. The extension theorem for a Besov space with respect to a lower Ahlfors measure 7990
- Chapter 10. Traces on the boundary of (ε, δ) domains 8596
- Chapter 11. The embedding of B[sup(p)][sub(β)](Ω, dμ) into L[sup(q)](Ω, dμ) 93104
- Chapter 12. Returning to Carnot groups 99110
- Chapter 13. The Neumann problem 103114
- Chapter 14. The case of Lipschitz vector fields 109120
- Bibliography 111122