Read e-book online Analytic Capacity, the Cauchy Transform, and Non-homogeneous PDF

By Xavier Tolsa

This booklet experiences the various groundbreaking advances which were made concerning analytic capability and its courting to rectifiability within the decade 1995–2005. The Cauchy remodel performs a primary position during this region and is for that reason one of many major matters coated. one other very important subject, that may be of autonomous curiosity for lots of analysts, is the so-called non-homogeneous Calderón-Zygmund concept, the improvement of which has been mostly encouraged through the issues bobbing up in reference to analytic capability. 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 instrument within the learn of this challenge. within the Sixties Vitushkin conjectured that the detachable units that have finite size coincide with these that are merely unrectifiable. furthermore, as a result of the purposes to the idea of uniform rational approximation, he posed the query as to if analytic potential 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 similar questions also are mentioned, akin to the connection among rectifiability and the lifestyles of central values for the Cauchy transforms and different singular integrals. The booklet is essentially self-contained and will be obtainable for graduate scholars in research, in addition to a priceless 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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