## 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].

### MSC:

 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