Boundedness of the differentiation operator in model spaces and application to Peller type inequalities

Anton Baranov (1) , Rachid Zarouf (2)

1 Department of Mathematics and Mechanics
2 Mathématiques Fondamentales

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 $\overline{\mathbb{D}}$.

Mots clés: Rational function; Peller's inequality; Besov norm; weighted Bergman norm; model space; Blaschke product

Domaines: Analyse fonctionnelle [math.FA]

Anton Baranov, Rachid Zarouf. Boundedness of the differentiation operator in model spaces and application to Peller type inequalities. 2014. ⟨hal-01044624v2⟩