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// Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
// Archive
Mat. Fiz. Anal. Geom.,
2000
Volume 7,
Number 1,
Pages
119–127
(Mi jmag397)
On the Cauchy transform of the Bergman space
S. A. Merenkov
Department of Mathematics and Mechanics, Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine
Abstract:
The range of the Bergman space
$B_2(G)$
under the Cauchy transform
$K$
is described for a large class of domain. For a quasidisk
$G$
the relation $ K(B_2^*(G))=B_2^1(\mathbb C\setminus\overline G)$ is proved.
Received:
03.04.1998
Language:
English
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Steklov Math. Inst. of RAS
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