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Hankel operators on weighted Bergman spaces. (English) Zbl 0669.47017
The authors study Hankel operators on weighted Bergman spaces and establishes the connection between an analytic function f and the Hankel operator generated by f on certain weighted Bergman spaces consisting of analytic functions on the unit disk $$\Delta$$.
Contents. Introduction. 1. Background. 2. General properties of Hankel operators. 3. Hilbert-Schmidt-Hankel operators and Dirichlet space. 4. Boundedness and compactness of $$H_ f$$. 5. The space $$B_ 1$$, the Macaev ideal, and Hankel operators. 6. Hankel operators in $$S_ p$$ and $$B_ p$$, $$2<p<\infty$$. 7. The case $$1<p<2$$ and $$0\leq \alpha$$. 8. The case $$-1<\alpha <0$$, $$1<p<2$$. 9. The reduced Hankel operator. 10. Hankel operators with non analytic symbols 11. Hankel operators as vector-valued paracommutators.
Some results of this paper were earlier announced in the authors’ work “Hankel operators on the Bergman space”. Abstr. Pap. Am. Math. Soc. 7, 163 (1986).
Reviewer: N.K.Karapetianc

##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces
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