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

# metadata.dc.description.abstract[].value
In \cite{Aleman:Cascante:Fabrega:Pascuas:Pelaez} it is shown that the Bloch space $\mathcal{B}$ in the unit disc has the following

radicality property: if an analytic function $g$ satisfies that $g^n\in \mathcal{B}$, then $g^m\in \mathcal{B}$, for all $m\le n$. Since $\mathcal{B}$ coincides with the space $\mathcal{T}(A^p_\alpha)$ of analytic symbols $g$ such that the Volterra-type operator

$T_gf(z)= \int_0^z f(\zeta)g'(\zeta)\,d\zeta$

is bounded on the classical weighted Bergman space $A^p_\alpha$, the radicality property was used to study the composition of paraproducts $T_g$ and $S_gf=T_fg$ on $A^p_{\alpha}$. Motivated by this fact, we prove that $\mathcal{T}(A^p_\omega)$ also has the radicality property, for any radial weight $\omega$. Unlike the classical case,

the lack of a precise description of $\mathcal{T}(A^p_\omega)$ for a general radial weight, induces us to prove the radicality property for $A^p_\omega$ from precise norm-operator results for compositions of analytic paraproducts.

# metadata.dc.relation.ispartof[].value
Journal of Functional Analysis, 2024, vol. 287, num.12

# metadata.dc.rights[].value
cc by-nc-nd (c) Carme Cascante et al., 2024

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
On the radicality property for spaces of symbols of bounded Volterra operators