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

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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. 
@article{ZNSL_2022_512_a8,
     author = {P. A. Mozolyako},
     title = {$B$-points of a {Cantor-type} set},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {148--172},
     publisher = {mathdoc},
     volume = {512},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a8/}
}
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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/