Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory

種類:

電子ブック

責任表示:

by Xavier Tolsa

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2014

著者名:

• Tolsa, Xavier
• SpringerLink (Online service)

シリーズ名:

Progress in Mathematics ; 307

ISBN:

9783319005966 [3319005960]    

注記:

This 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

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