000			03653nam a22003735i 4500
001			292175
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007			cr nn 008mamaa
008			150903s2014 gw | o |||| 0|eng d
020			_a9783319005966 _99783319005966
024	7		_a10.1007/9783319005966 _2doi
035			_avtls000345713
039		9	_a201509030907 _bVLOAD _c201405050324 _dVLOAD _y201402061342 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA331-355
100	1		_aTolsa, Xavier. _eautor _9323767
245	1	0	_aAnalytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory / _cby Xavier Tolsa.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Birkhäuser, _c2014.
300			_axiii, 396 páginas 8 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aProgress in Mathematics, _x0743-1643 ; _v307
500			_aSpringer eBooks
505	0		_aIntroduction -- Basic notation -- Chapter 1. Analytic capacity -- Chapter 2. Basic Calderón-Zygmund theory with non doubling measures -- Chapter 3. The Cauchy transform and Menger curvature -- Chapter 4. The capacity ?+ -- Chapter 5. A Tb theorem of Nazarov, Treil and Volberg -- Chapter 6. The comparability between ? and ? +, and the semiadditivity of analytic capacity -- Chapter 7. Curvature and rectifiability -- Chapter 8. Principal values for the Cauchy transform and rectifiability -- Chapter 9. RBMO(?) and H1 atb(?) -- Bibliography -- Index.
520			_aThis book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Calderón-Zygmund theory, the development of which has been largely motivated by the problems arising in connection with analytic capacity. The Painlevé problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metric and geometric terms. Analytic capacity is a key tool in the study of this problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover, because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkin’s conjecture and of the semiadditivity of analytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, such as the relationship between rectifiability and the existence of principal values for the Cauchy transforms and other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuable resource for researchers.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9783319005959
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-319-00596-6 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c292175 _d292175