On the radicality property for spaces of symbols of bounded Volterra operators

Abstract

In [1] it is shown that the Bloch space in the unit disc has the following radicality property: if an analytic function g satisfies that , then , for all . Since coincides with the space of analytic symbols g such that the Volterra-type operator is bounded on the classical weighted Bergman space , the radicality property was used to study the composition of paraproducts and on . Motivated by this fact, we prove that also has the radicality property, for any radial weight ω. Unlike the classical case, the lack of a precise description of for a general radial weight, induces us to prove the radicality property for from precise norm-operator results for compositions of analytic paraproducts.