A Volterra type operator on spaces of analytic functions. (English) Zbl 0955.47029

Jarosz, Krzysztof (ed.), Function spaces. Proceedings of the 3rd conference, Edwardsville, IL, USA, May 19-23, 1998. Providence, RI: American Mathematical Society. Contemp. Math. 232, 299-311 (1999).
The article studies properties of Volterra type operators in the functional spaces. There are two parts in the paper.
The first part describes general propositions for linear operators \[ I_g(f)(z)= \int^z_0 f(\zeta) g'(\zeta) d\zeta. \] This operator is acting on a Banach space of analytic functions defined on the unit disc in the complex plane \(\mathbb{C}\).
In the second part the operator is acting on BMOA spaces. The terms for \(I_g\) are found when the operator \(I_g\) is bounded or compact. About the operator \(I_g\) on Hardy spaces \(H^p\) see [A. Aleman and A. G. Siskakis, Complex Variables, Theory Appl. 28, No. 2, 149-158 (1995; Zbl 0837.30024)]. About the operator \(I_g\) on Bergman spaces see [A. Aleman and A. G. Siskakis, Indiana Univ. Math. J. 46, No. 2, 337-356 (1997))].
For the entire collection see [Zbl 0913.00036].


47G10 Integral operators
47B38 Linear operators on function spaces (general)
46E15 Banach spaces of continuous, differentiable or analytic functions
47B07 Linear operators defined by compactness properties
30D55 \(H^p\)-classes (MSC2000)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces


Zbl 0837.30024