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.

UDC: 517.55

Received: 19.01.2012

Language: English