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arXiv · 1711.02717

The Stieltjes integrals in the theory of harmonic and analytic functions

Vladimir Ryazanov
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Abstract

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 $2\pi -$periodic bounded integrands that are differentiable a.e. and, in particular, for integrands of the class ${\cal {CBV}}$ (countably bounded variation).

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Vladimir Ryazanov. 2017-11-07. The Stieltjes integrals in the theory of harmonic and analytic functions. https://arxiv.org/abs/1711.02717

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