Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2015, Volume 11, Number 3, Pages 236–244
DOI: https://doi.org/10.15407/mag11.03.236 (Mi jmag618) 		 
On the growth of the Cauchy–Szegő transform in the unit ball

I. Chyzhykov, M. Voitovych

Faculty of Mechanics and Mathematics, Lviv Ivan Franko National University, 1 Universytetska Str., Lviv 79000, Ukraine
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DOI: https://doi.org/10.15407/mag11.03.236
Abstract: The growth of analytic and harmonic functions in the unit ball $B_n$ represented by the Cauchy–Stieltjes or Poisson–Stieltjes integral is studied. A description of the growth is given in terms of smoothness of the Stieltjes measure.
Key words and phrases: holomorphic function, Cauchy–Szegő transform, modulus of continuity, Lipschitz class, Poisson integral, Cauchy integral, Cauchy–Stieltjes integral, Poisson–Stielstjes integral, unit ball.
Received: 22.09.2014
Revised: 14.01.2015
Bibliographic databases:
Document Type: Article
MSC: Primary 32A26; Secondary 32A25
Language: English
Citation: I. Chyzhykov, M. Voitovych, “On the growth of the Cauchy–Szegő transform in the unit ball”, Zh. Mat. Fiz. Anal. Geom., 11:3 (2015), 236–244
Citation in format AMSBIB
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\by I.~Chyzhykov, M.~Voitovych
\paper On the growth of the Cauchy--Szeg\H{o} transform in the unit ball
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2015
\vol 11
\issue 3
\pages 236--244
\mathnet{http://mi.mathnet.ru/jmag618}
\crossref{https://doi.org/10.15407/mag11.03.236}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3443273}
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