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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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