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- W2613851296 abstract "The problem of describing the range of a Bergman space B_2(G) under the Cauchy transform K for a Jordan domain G was solved by Napalkov (Jr) and Yulmukhametov. It turned out that K(B_2(G))=B_2^1(Cbar G) if and only if G is a quasidisk; here B_2^1(Cbar G) is the Dirichlet space of the complement of bar G. The description of K(B_2(G)) for an integrable Jordan domain is given in [S. Merenkov, On the Cauchy transform of the Bergman space, Mat. Fiz. Anal. Geom., 7 (2000), no. 1, 119-127]. In the present paper we give a description of K(B_2(G,omega)) analogous to the one given in [S. Merenkov, On the Cauchy transform of the Bergman space, Mat. Fiz. Anal. Geom., 7 (2000), no. 1, 119-127] for a weighted Bergman space B_2(G,omega) with a weight omega which is constant on level lines of the Green function of G. In the case G=D, the unit disk, and under some additional conditions on the weight omega, K(B_2(D,omega))=B_2^1(Cbar{D}, omega^{-1}), a weighted analogue of a Dirichlet space." @default.
- W2613851296 created "2017-05-19" @default.
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- W2613851296 date "2013-05-18" @default.
- W2613851296 modified "2023-09-27" @default.
- W2613851296 title "On the Cauchy transform of weighted Bergman spaces" @default.
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