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Stieltjes Integrals in the Theory of Harmonic Functions

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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).

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Slavyansk, Ukraine

    V. I. Ryazanov

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  1. V. I. Ryazanov
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Correspondence to V. I. Ryazanov.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 467, 2018, pp. 151–168.

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Ryazanov, V.I. Stieltjes Integrals in the Theory of Harmonic Functions. J Math Sci 243, 922–933 (2019). https://doi.org/10.1007/s10958-019-04593-3

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  • DOI: https://doi.org/10.1007/s10958-019-04593-3

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