Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carath�eodory spaces / [electronic resource] Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu.

By: Danielli, Donatella, 1966-Contributor(s): Garofalo, Nicola | Nhieu, Duy-Minh, 1966-Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 857Publication details: Providence, R.I. : American Mathematical Society, c2006Description: 1 online resource (ix, 119 p.)ISBN: 9781470404611 (online)Subject(s): Harmonic analysis | Homogeneous spaces | Sobolev spaces | Measure theory | Differential equations, PartialAdditional physical formats: Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carath�eodory spaces /DDC classification: 510 s | 515/.2433 LOC classification: QA3 | .A57 no. 857 | QA403Online resources: Contents | Contents
Contents:
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
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"July 2006, volume 182, number 857 (first of 4 numbers)."

Includes bibliographical references (p. 111-119).

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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