Given an inner function $\Theta$ in the unit disc $\mathbb{ D}$, we study the boundedness of the differentiation operator which acts from from the model subspace $K\_{ \Theta}=\left(\Theta H^{ 2}\right)^{ \perp}$ of the Hardy space $H^{ 2},$ equiped with the $BMOA$-norm, to some radial-weighted Bergman space. As an application, we generalize Peller's inequality for Besov norms of rational functions $f$ of degree $n\geq1$ having no poles in the closed unit disc $\overline{ \mathbb{ D}}$.
Categories: math.FA