The Cauchy–Stieltjes integrals in the theory of analytic functions
- Авторлар: Ryazanov V.1
-
Мекемелер:
- Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
- Шығарылым: Том 234, № 1 (2018)
- Беттер: 61-72
- Бөлім: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241754
- DOI: https://doi.org/10.1007/s10958-018-3981-z
- ID: 241754
Дәйексөз келтіру
Аннотация
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).
Авторлар туралы
Vladimir Ryazanov
Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
Хат алмасуға жауапты Автор.
Email: vl.ryazanov1@gmail.com
Украина, Slavyansk