Geodesic
On the Cauchy transform of the Bergman space
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 1, pp. 119-127 
S. A. Merenkov. On the Cauchy transform of the Bergman space. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 1, pp. 119-127. http://geodesic.mathdoc.fr/item/JMAG_2000_7_1_a6/
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     author = {S. A. Merenkov},
     title = {On the {Cauchy} transform of the {Bergman} space},
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     year = {2000},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2000_7_1_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.