Cascante, Ma. Carme (Maria Carme)Fàbrega Casamitjana, JoanPascuas Tijero, DanielPeláez Márquez, José Ángel2025-02-192025-02-192024-12-150022-1236https://hdl.handle.net/2445/218955<p>In \cite{Aleman:Cascante:Fabrega:Pascuas:Pelaez} it is shown that the Bloch space $\mathcal{B}$ in the unit disc has the following </p><p>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  </p><p>$T_gf(z)= \int_0^z f(\zeta)g'(\zeta)\,d\zeta$</p><p> 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, </p><p>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.</p>29 p.application/pdfengcc by-nc-nd (c) Carme Cascante et al., 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/Espais de HardyOperadors integralsEspais analíticsFuncions de variables complexesHardy spacesIntegral operatorsAnalytic spacesFunctions of complex variablesinfo:eu-repo/semantics/article7545632025-02-19info:eu-repo/semantics/openAccess