For a fixed analytic function $g$ on the unit $\mathbb{D}$, we consider the analytic paraproducts induced by $g$, which are defined by
$T_gf(z)= \int_0^z f(\zeta)g'(\zeta)\,d\zeta$,
$S_gf(z)= \int_0^z f'(\zeta)g(\zeta)\,d\zeta$, and
$M_gf(z)= f(z)g(z)$.

We will present a characterization of the boundedness of a large class of operators contained in the algebra
generated by these analytic paraproducts acting on the classical weighted Bergman and Hardy spaces in terms of the symbol $g$.

This is a joint work together with A. Aleman, C. Cascante, J. Fábrega and D. Pascuas