The Cauchy–Stieltjes integrals in the theory of analytic functions
- 作者: Ryazanov V.1
-
隶属关系:
- Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
- 期: 卷 234, 编号 1 (2018)
- 页面: 61-72
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241754
- DOI: https://doi.org/10.1007/s10958-018-3981-z
- ID: 241754
如何引用文章
详细
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).
作者简介
Vladimir Ryazanov
Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
编辑信件的主要联系方式.
Email: vl.ryazanov1@gmail.com
乌克兰, Slavyansk