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The Cauchy–Stieltjes integrals in the theory of analytic functions

  • Vladimir I. Ryazanov
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Abstract

We study various Stieltjes integrals as Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz–Stieltjes, and Cauchy–Stieltjes ones and prove theorems on the existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes integral. These results hold for arbitrary bounded integrands that are differentiable a.e. and, in particular, for integrands of the class \( \mathcal{C}\mathrm{\mathcal{B}}\mathcal{V} \) (countably bounded variation).

Keywords

Stieltjes Poisson–Stieltjes Schwartz–Stieltjes Cauchy–Stieltjes and Hilbert–Stieltjes integrals harmonic and analytic functions angular limits 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and Mechanics of the NAS of UkraineSlavyanskUkraine

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