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

DOI:
https://doi.org/10.1090/S0002-9939-1994-1189752-0

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1189752-0

Keywords:
Harmonic measure,
positive harmonic function in half-plane,
capacity

Article copyright:
© Copyright 1994
American Mathematical Society