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An elementary proof of Benedicks’s and Carleson’s estimates of harmonic measure of linear sets

Author: Mikhail Sodin
Journal: Proc. Amer. Math. Soc. 121 (1994), 1079-1085
MSC: Primary 30C85; Secondary 31A15
MathSciNet review: 1189752
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Abstract: Benedicks and Carleson proved sophisticated estimates of harmonic measure of linear sets which have found applications in approximation theory and harmonic analysis. We give an elementary proof of these estimates. This proof allows us to relax the assumptions and strengthen estimates.

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Keywords: Harmonic measure, positive harmonic function in half-plane, capacity
Article copyright: © Copyright 1994 American Mathematical Society