The Stieltjes integrals in the theory of harmonic functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 151-168 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study various Stieltjes integrals, such as Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz–Stieltjes and Cauchy–Stieltjes, and prove theorems on the existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes integral. These results are valid for arbitrary bounded integrands that are differentiable a.e. and, in particular, for integrands of the class $\mathcal{CBV}$ (countably bounded variation).
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V. Ryazanov. The Stieltjes integrals in the theory of harmonic functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 151-168. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a13/

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