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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 166–172 (Mi ufa143)  

On the asymptotic behavior of Cauchy–Stieltjes integral in the polydisc

O. A. Zolota

Institute of Physics, Mathematics and Computer Science, Drohobych Ivan Franko State Pedagogical University, Drohobych, Lviv reg., Ukraine

Abstract: In the paper the asymptotic behavior of Cauchy–Stieltjes integral of a complex-valued Borel measure on the skeleton in the polydisc is described. The main result holds outside a set of zero $\omega$-capacity. It generalizes the theorem for the one-dimensional case.

Keywords: modulus of continuity, Cauchy–Stieltjes integral, polydisc, set of zero $\omega$-capacity, non-tangential limit.

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UDC: 517.55
Received: 19.01.2012
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Citation: O. A. Zolota, “On the asymptotic behavior of Cauchy–Stieltjes integral in the polydisc”, Ufimsk. Mat. Zh., 4:1 (2012), 166–172

Citation in format AMSBIB
\Bibitem{Zol12}
\by O.~A.~Zolota
\paper On the asymptotic behavior of Cauchy--Stieltjes integral in the polydisc
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 166--172
\mathnet{http://mi.mathnet.ru/ufa143}


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