# Bornitude de l’opérateur de dérivation dans les espaces modèles et applications aux inégalités de Peller

Rachid Zarouf
I2M, Aix-Marseille Université
/user/rachid.zarouf/

Date(s) : 03/11/2014   iCal
10 h 00 min - 11 h 00 min

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

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

https://hal.archives-ouvertes.fr/hal-01044624v2/

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