Geodesic
On the definition of $B$-points of a Borel charge on the real line
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 191-205 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mu$ be a Borel charge (i.e., a real Borel measure) on $\mathbb R$, and let $P_{(y)}(t)=\frac y{\pi(y^2+t^2)}$, $y>0$, $t\in\mathbb R$, denote the Poisson kernel. Bourgain proved in [1,2] that for a nonnegative $\mu$ and for numerous $x\in\mathbb R$ the variation of the function $y\mapsto(\mu*P_{(y)})(x)$ on $(0,1]$ is finite. This is true in particular for the so-called $B$-points $x$ (see e.g., [4]). In the present article new descriptions of $B$-points are given adjusted to some applications of this notion. 
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     author = {P. A. Mozolyako},
     title = {On the definition of $B$-points of {a~Borel} charge on the real line},
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P. A. Mozolyako. On the definition of $B$-points of a Borel charge on the real line. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 191-205. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a10/

[1] Zh. Burgein, “Ogranichennost variatsii svërtok mer”, Matem. zametki, 54:4 (1993), 24–33 | MR | Zbl

[2] J. Bourgain, “On the radial variation of bounded analytic functions on the disk”, Duke Math. J., 69:3 (1993), 671–682 | DOI | MR | Zbl

[3] P. A. Mozolyako, “Zamechaniya k opredeleniyu tochek Burgeina”, Zap. nauchn. semin. POMI, 355, 2008, 219–236 | MR

[4] P. A. Mozolyako,, “Usilennaya skhodimost approksimativnykh edinits i tochki Burgeina ogranichennykh funktsii”, Dokl. RAN, 422:6 (2008), 738–740 | MR | Zbl

[5] P. A. Mozolyako, Tochki Burgeina na mnozhestve kantorovskogo tipa, Preprint