%0 Unpublished work
%T Boundedness of the differentiation operator in model spaces and application to Peller type inequalities
%+ Department of Mathematics and Mechanics
%+ Mathématiques Fondamentales
%A Baranov, Anton
%A Zarouf, Rachid
%8 2014-07-23
%D 2014
%Z 1407.6347
%K Rational function
%K Peller's inequality
%K Besov norm
%K weighted Bergman norm
%K model space
%K Blaschke product
%Z Primary 32A36, 26A33; Secondary 26C15, 41A10
%Z Mathematics [math]/Functional Analysis [math.FA]Preprints, Working Papers, ...
%X 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 $\overline{\mathbb{D}}$.
%G English
%2 https://hal.science/hal-01044624v2/document
%2 https://hal.science/hal-01044624v2/file/peller_final.pdf
%L hal-01044624
%U https://hal.science/hal-01044624
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ ESPE-AMU_PUBLICATIONS