This article is cited in 4 papers

Growth of the Poisson–Stieltjes integral in a polydisc

I. Chyzhykov^a, O. Zolota<sup>b

a</sup> Faculty of Mechanics and Mathematics, Lviv Ivan Franko National University, 1, Universytetska Str., Lviv, 79000, Ukraine
^b Institute of Physics, Mathematics and Computer Science, Drohobych Ivan Franko State Pedagogical University, 24, I. Franko Str., Drohobych 82100, Ukraine

Abstract: We describe the growth of the value $M_{\infty}(r_1,\dots,r_n,v)=\max\{|v\ (z_1,\dots,z_n)|:|z_j|\le r_j\}$, $0\le r_j<1$ in terms of the modulus of continuity of a measure $\mu$, where the function $v$ is represented by the Poisson–Stieltjes integral.

Key words and phrases: modulus of continuity, multiple Poisson kernel, Poisson–Stieltjes integral, polydisc.

MSC: 31B05, 31B10, 32A22, 32A25, 32A26, 32A35

Received: 11.06.2010

Language: English

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