Composition of analytic paraproducts
Composition of analytic paraproducts
For a fixed analytic function $g$ on the unit disc $\mathbb{D}$, 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 $M_gf(z)= f(z)g(z)$. The boundedness of these operators on various spaces of analytic functions on $\mathbb{D}$ is well understood. The original …