The Cauchy–Stieltjes integrals in the theory of analytic functions
- Authors: Ryazanov V.I.1
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Affiliations:
- Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
- Issue: Vol 234, No 1 (2018)
- Pages: 61-72
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241754
- DOI: https://doi.org/10.1007/s10958-018-3981-z
- ID: 241754
Cite item
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).
About the authors
Vladimir I. Ryazanov
Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
Author for correspondence.
Email: vl.ryazanov1@gmail.com
Ukraine, Slavyansk