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arXiv · 1407.6347

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

Anton Baranov·Rachid Zarouf
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Abstract

Given an inner function $Θ$ in the unit disc $\mathbb{D}$, we study the boundedness of the differentiation operator which acts from from the model subspace $K\_Θ=\left(ΘH^{2}\right)^{\perp}$ 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 $\overline{\mathbb{D}}$.

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Anton Baranov, Rachid Zarouf. 2016-01-11. Boundedness of the differentiation operator in model spaces and application to Peller type inequalities. https://arxiv.org/abs/1407.6347

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