2017/11/07 by Vladimir Ryazanov, Ryazanov, Vladimir
Mathematics · #31A05 #31A20 #31A25 #31B25 #31C05 #34M50 #35F45 #35Q15 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Primary 30C62 #Secondary 30E25
paper · pdf · doi:10.48550/arxiv.1711.02717
openalex publication_date 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular Hilbert-Stieltjes integral in the sense of the principal value. These results hold for arbitrary 2π-periodic bounded integrands that are differentiable a.e. and, in particular, for integrands of the class \cal CBV (countably bounded variation).