Get Analytic Capacity, the Cauchy Transform, and Non-homogeneous PDF

By Xavier Tolsa

ISBN-10: 3319005952

ISBN-13: 9783319005959

This e-book reviews the various groundbreaking advances which have been made relating to analytic ability and its courting to rectifiability within the decade 1995–2005. The Cauchy rework performs a primary position during this sector and is consequently one of many major matters lined. one other vital subject, that may be of self reliant curiosity for lots of analysts, is the so-called non-homogeneous Calderón-Zygmund conception, the advance of which has been mostly encouraged by means of the issues bobbing up in reference to analytic potential. The Painlevé challenge, which was once first posed round 1900, is composed to find an outline of the detachable singularities for bounded analytic services in metric and geometric phrases. Analytic means is a key device within the research of this challenge. within the Nineteen Sixties Vitushkin conjectured that the detachable units that have finite size coincide with these that are simply unrectifiable. in addition, as a result of purposes to the speculation of uniform rational approximation, he posed the query to whether analytic ability is semiadditive. This paintings offers complete proofs of Vitushkin’s conjecture and of the semiadditivity of analytic potential, either one of which remained open difficulties till very lately. different comparable questions also are mentioned, equivalent to the connection among rectifiability and the lifestyles of valuable values for the Cauchy transforms and different singular integrals. The publication is basically self-contained and will be available for graduate scholars in research, in addition to a precious source for researchers.

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Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory: 307 (Progress in Mathematics) by Xavier Tolsa

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