On the growth of the Cauchy–Szegő transform in the unit ball
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 3, pp. 236-244 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
@article{JMAG_2015_11_3_a1,
     author = {I. Chyzhykov and M. Voitovych},
     title = {On the growth of the {Cauchy{\textendash}Szeg\H{o}} transform in the unit ball},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {236--244},
     year = {2015},
     volume = {11},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2015_11_3_a1/}
}
TY  - JOUR
AU  - I. Chyzhykov
AU  - M. Voitovych
TI  - On the growth of the Cauchy–Szegő transform in the unit ball
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2015
SP  - 236
EP  - 244
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2015_11_3_a1/
LA  - en
ID  - JMAG_2015_11_3_a1
ER  - 
%0 Journal Article
%A I. Chyzhykov
%A M. Voitovych
%T On the growth of the Cauchy–Szegő transform in the unit ball
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2015
%P 236-244
%V 11
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2015_11_3_a1/
%G en
%F JMAG_2015_11_3_a1
I. Chyzhykov; M. Voitovych. On the growth of the Cauchy–Szegő transform in the unit ball. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 3, pp. 236-244. http://geodesic.mathdoc.fr/item/JMAG_2015_11_3_a1/

[1] Sh. Chen, A. Rasila, X. Wang, “Radial Growth, Lipschitz and Dirichlet Spaces on Solutions to the Nonhomogenous Yukawa Equation”, Israel J. Math., 204:1 (2014), 261–282 | MR | Zbl

[2] Sh. Chen, M. Mateljevic, S. Ponnusamy, X. Wang, Lipschitz Type Spaces and Landau–Bloch Type Theorems for Harmonic Functions and Poisson Equations, 2014, arXiv: 1407.7179

[3] I. E. Chyzhykov, “Growth and Representation of Analytic and Harmonic Functions in the Unit Disc”, Ukrainian Math. Bull., 3:1 (2006), 31–44 | MR | Zbl

[4] I. E. Chyzhykov, O. A. Zolota, “Sharp Estimates of the Growth of the Poisson–Stieltjes Integral in the Polydisc”, Mat. Stud., 2010, no. 2, 193–196 | MR | Zbl

[5] I. E. Chyzhykov, O. A. Zolota, “Growth of the Poisson–Stieltjes Integral in the Polydisc”, J. Math. Phys. Anal. Geom., 7:2 (2011), 141–157 | MR | Zbl

[6] P. Duren, Theory of $H^p$ Spaces, Academic Press, New York, 1970 | MR

[7] K. T. Hahn, J. Mitchell, “Representation of Linear Functionals in $H^p$-spaces over Bounded Symmetric Domains in $\mathbb{C}^n$”, J. Math. Anal. Appl., 56:22 (1976), 379–396 | MR | Zbl

[8] G. H. Hardy, J. E. Littlewood, “A Convergence Criterion for Fourier Series”, Math. Z., 28:4 (1928), 612–634 | MR | Zbl

[9] S. G. Kranz, “Lipschitz Spaces, Smoothness of Functions, and Approximation Theory”, Expo. Math., 3 (1983), 193–260 | MR

[10] W. Rudin, Function Theory in the Unit ball of $\mathbb{C}^n$, Springer-Verlag, Berlin–Heidelberg–New York, 1980 | MR

[11] M. Stoll, Invariant Potential Theory in the Unit Ball of $\mathbb{C}^n$, Cambridge Univ. Press, Cambridge, 1994 | MR