Growth of p-th means of the Poisson-Stieltjes integrals in polydisc

Author
I. E. Chyzhykov1, O. A. Kutnyak2
1) Faculty of Mechanics and Mathematics Lviv Ivan Franko National University; 2) Institute of Physics, Mathematics, Economics and Innovative Technologies Drohobych Ivan Franko State Pedagogical University
Abstract
We prove a sharp upper estimate of the $p$th means of the Poisson-Stieltjes integrals in the unit polydisc for $p>1$. The estimate is given in terms of the smoothness of a complex-valued Stieltjes measure $\mu$. If the measure $\mu$ is positive, the estimate becomes equivalent to the smoothness condition.
Keywords
Poisson-Stieltjes integral; p-th means; unit polydisc; integral modulus of continuity; complexvalued Stieltjes measure; growth
DOI
doi:10.30970/ms.52.1.48-54
Reference
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3. Chyzhykov I., Voitovych M. Growth description of pth means of the Green potential in the unit ball// Complex Variables and Elliptic Equations. 2017. V.62, 7. P. 899913.

4. Chyzhykov I.E., Zolota O.A. Sharp estimates of the growth of the Poisson-Stieltjes integral in the polydisc// Mat. Stud. 2010. V.34, 2. P. 193196. Corrections in Mat. Stud. 2012. V.37, 2. P. 223224.

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Pages
48-54
Volume
52
Issue
1
Year
2019
Journal
Matematychni Studii
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