---

＜電子ブック＞
Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral / by Hervé M. Pajot
(Lecture Notes in Mathematics. ISSN:16179692 ; 1799)

版	1st ed. 2002.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2002
大きさ	VIII, 119 p : online resource
著者標目	*Pajot, Hervé M author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Geometry LCSH:Measure theory LCSH:Functions of complex variables LCSH:Fourier analysis FREE:Analysis FREE:Geometry FREE:Measure and Integration FREE:Functions of a Complex Variable FREE:Fourier Analysis
一般注記	Preface -- Notations and conventions -- Some geometric measures theory -- Jones' traveling salesman theorem -- Menger curvature -- The Cauchy singular integral operator on Ahlfors-regular sets -- Analytic capacity and the Painlevé Problem -- The Denjoy and Vitushkin conjectures -- The capacity $gamma (+)$ and the Painlevé Problem -- Bibliography -- Index Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem HTTP:URL=https://doi.org/10.1007/b84244

 類似資料