A criterion on a subdomain of the disc for its harmonic measure to be comparable with Lebesgue measure
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- by A. L. Vol′berg PDF
- Proc. Amer. Math. Soc. 112 (1991), 153-162 Request permission
Abstract:
A subdomain $O$ of the disc $\mathbb {D}$ is called a boundary layer if $\omega (O, \cdot ) \geq \alpha \cdot m$, where $\omega (O, \cdot )$ is the harmonic measure of $O$. The metric criterion in terms of $\partial O$ is given for the case when $\alpha$ is near 1.References
- A. A. Borichev and A. L. Vol′berg, Uniqueness theorems for almost analytic functions, Algebra i Analiz 1 (1989), no. 1, 146–177 (Russian); English transl., Leningrad Math. J. 1 (1990), no. 1, 157–191. MR 1015338
- Lennart Carleson, Selected problems on exceptional sets, Van Nostrand Mathematical Studies, No. 13, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0225986 M. Essèn, On minimal thinness, reduced functions and Green potentials, Upp. Univ. Dep. Math., no. 13, 1989.
- James E. Thomson, Approximation in the mean by polynomials, Ann. of Math. (2) 133 (1991), no. 3, 477–507. MR 1109351, DOI 10.2307/2944317 A. L. Volberg, The logarithm of an almost analytic function is summable, Soviet Math. Dokl. 26 (1982), 238-243.
- A. L. Vol′berg and B. Ërikke, Summability of the logarithm of an almost analytic function and generalization of the Levinson-Cartwright theorem, Mat. Sb. (N.S.) 130(172) (1986), no. 3, 335–348, 431 (Russian); English transl., Math. USSR-Sb. 58 (1987), no. 2, 337–349. MR 865765
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 153-162
- MSC: Primary 31A15; Secondary 30C85
- DOI: https://doi.org/10.1090/S0002-9939-1991-1045152-2
- MathSciNet review: 1045152