Abstract
Harmonic measure is one of the basic objects of one dimensional complex analysis. Recently the structure of harmonic measure of rather general plane sets became much more comprehensible due to works of Makarov [1], Carleson [2] and Jones, Wolff [3]. The deep analogy between the behaviour of sums of (almost) independent random variables and the behaviour of the Green function of a domain plays a crucial role in this subject. We refer the reader to [15] for more details. This analogy becomes still more conspicuous if the domain for which the harmonic measure is investigated has regular self-similar structure. The methods of ergodic theory turn out to be relevant in this case, see e.g. [2], [4], [5], [6].
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© 1992 Springer Science+Business Media New York
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Volberg, A.L. (1992). On the Harmonic Measure of Self-Similar Sets on the Plane. In: Picardello, M.A. (eds) Harmonic Analysis and Discrete Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2323-3_22
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DOI: https://doi.org/10.1007/978-1-4899-2323-3_22
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