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Analysis and PDE Seminar

Date:
-
Location:
TBA
Speaker(s) / Presenter(s):
Professor Vladimir Eiderman, Indiana University Bloomington

Title:  Almost additivity of analytic capacity and boundedness of Cauchy operators

Abstract:  The notion of analytic capacity was introduced in 1947 by Ahlfors in connection with the celebrated Painlev\'e problem: describe in metric/geometric terms the sets of removable singularities for bounded analytic functions. We give a shot survey of results and methods of this theory. They allow us to prove that under certain assumptions the analytic capacity of a union of sets is comparable with the sum of their analytic capacities. As an application we consider the problem of boundedness of the Cauchy operator generated by a union of measures, if the Cauchy operators of these measures are uniformly bounded. The results obtained jointly with Alexander Reznikov and Alexander Volberg.