Geodesic
$B$-points of a Cantor-type set
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 148-172 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this note we study the behavior of the harmonic continuation $u$ to the upper half-plane for the characteristic function of a Cantor-type set $E$ of positive length, which is precisely the harmonic measure of such a set, near the boundary. We are interested in the description of points $x\in E$ (given in terms of their Cantor encoding) such that the mean variation of $u$ along $[x,x+i]$ – a certain weighted average of variations along $[x,x+t+i]$, $t\in\mathbb{R}$ – is finite. 
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     title = {$B$-points of a {Cantor-type} set},
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P. A. Mozolyako. $B$-points of a Cantor-type set. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 148-172. http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a8/

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