Email this article Stieltjes Integrals in the Theory of Harmonic Functions
- Authors: Ryazanov V.I.1
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Affiliations:
- Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
- Issue: Vol 243, No 6 (2019)
- Pages: 922-933
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/243187
- DOI: https://doi.org/10.1007/s10958-019-04593-3
- ID: 243187
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Abstract
We study various Stieltjes integrals (Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz– Stieltjes, and Cauchy–Stieltjes integrals) 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 from the class CBV (countably bounded variation).
About the authors
V. I. Ryazanov
Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
Author for correspondence.
Email: vlryazanov1@rambler.ru
Ukraine, Slavyansk
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