TY  - BOOK
AU  - Danielli,Donatella
AU  - Garofalo,Nicola
AU  - Nhieu,Duy-Minh
TI  - Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carath�eodory spaces
T2  - Memoirs of the American Mathematical Society, 
SN  - 9781470404611 (online)
AV  - QA3QA403 .A57 no. 857
U1  - 510 s515/.2433 22
PY  - 2006///
CY  - Providence, R.I.
PB  - American Mathematical Society
KW  - Harmonic analysis
KW  - Homogeneous spaces
KW  - Sobolev spaces
KW  - Measure theory
KW  - Differential equations, Partial
N1  - "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; Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012
UR  - http://www.ams.org/memo/0857
UR  - http://dx.doi.org/10.1090/memo/0857
ER  -