000			04678nam a22005293i 4500
001			EBC3114232
003			MiAaPQ
005			20240729124603.0
006			m o d |
007			cr cnu||||||||
008			240724s2006 xx o ||||0 eng d
020			_a9781470404611 _q(electronic bk.)
020			_z9780821839119
035			_a(MiAaPQ)EBC3114232
035			_a(Au-PeEL)EBL3114232
035			_a(CaPaEBR)ebr11039851
035			_a(OCoLC)922981722
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA403 -- .D36 2006eb
082	0		_a510 s;515/.2433
100	1		_aDanielli, Donatella.
245	1	0	_aNon-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Carathéodory Spaces.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2006.
264		4	_c©2006.
300			_a1 online resource (138 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.182
505	0		_aIntro -- Contents -- Chapter 1. Introduction -- 1.1. Carnot-Carathéodory spaces -- 1.2. The Chow-Rashevsky's accessibility theorem and CC metrics -- 1.3. The Nagel-Stein-Wainger polynomial and the size of the CC balls -- Chapter 2. Carnot groups -- 2.1. Carnot groups of step 2 -- 2.2. The Kaplan mapping -- 2.3. Groups of Heisenberg type -- Chapter 3. The characteristic set -- 3.1. A result of Derridj on the size of the characteristic set -- 3.2. Some geometric examples -- 3.3. Non-characteristic manifolds -- 3.4. Manifolds with controlled characteristic set -- Chapter 4. X-variation, X-perimeter and surface measure -- 4.1. The structure of functions in BV[sub(X,loc)] -- 4.2. X-Caccioppoli sets -- 4.3. X-perimeter and the perimeter measure -- Chapter 5. Geometric estimates from above on CC balls for the perimeter measure -- 5.1. A fundamental estimate -- 5.2. The X-perimeter of a C[sup(1,1)] domain is an upper 1-Ahlfors measure -- Chapter 6. Geometric estimates from below on CC balls for the perimeter measure -- 6.1. The relative isoperimetric inequality and Theorem 6.1 -- 6.2. A basic geometric lemma -- 6.3. Further analysis for Hörmander vector fields of step 2 -- 6.4. Second proof of Theorem 6.1 -- 6.5. Failure of the 1-Ahlfors condition for the X-perimeter of C[sup(1,α)] domains -- Chapter 7. Fine differentiability properties of Sobolev functions -- 7.1. Poincaré inequality fractional integrals and improved representation formulas -- 7.2. Fine mapping properties of fractional integration on metric spaces -- 7.3. Differentiation with respect to an upper Ahlfors measure -- 7.4. Upper Ahlfors measures and Hausdorff measure -- Chapter 8. Embedding a Sobolev space into a Besov space with respect to an upper Ahlfors measure -- 8.1. Some results from harmonic analysis -- 8.2. Two simple growth-estimates.
505	8		_a8.3. A key continuity estimate for a singular integral -- 8.4. The main theorem -- Chapter 9. The extension theorem for a Besov space with respect to a lower Ahlfors measure -- 9.1. Some auxiliary results -- 9.2. Proof of Theorem 9.1 -- Chapter 10. Traces on the boundary of (ε, δ) domains -- 10.1. The (ε, δ) condition is optimal for the existence of traces -- 10.2. Characterization of the traces on the boundary -- Chapter 11. The embedding of B[sup(p)][sub(β)](Ω, dμ) into L[sup(q)](Ω, dμ) -- Chapter 12. Returning to Carnot groups -- Chapter 13. The Neumann problem -- Chapter 14. The case of Lipschitz vector fields -- Bibliography.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aHarmonic analysis.
650		0	_aHomogeneous spaces.
650		0	_aSobolev spaces.
650		0	_aMeasure theory.
650		0	_aDifferential equations, Partial.
655		4	_aElectronic books.
700	1		_aGarofalo, Nicola.
700	1		_aNhieum, Duy-Minh.
776	0	8	_iPrint version: _aDanielli, Donatella _tNon-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Carathéodory Spaces _dProvidence : American Mathematical Society,c2006 _z9780821839119
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114232 _zClick to View
999			_c69763 _d69763