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Journal d'Analyse Mathématique

, Volume 137, Issue 1, pp 189–209 | Cite as

The differentiation operator from model spaces to Bergman spaces and Peller type inequalities

  • Anton BaranovEmail author
  • Rachid Zarouf
Article
  • 39 Downloads

Abstract

Given an inner function Θ on the unit disc \(\mathbb{D}\), we study the boundedness of the differentiation operator which acts from the model subspace KΘ = (ΘH2) of the Hardy space H2, equipped 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 ≥ 1 having no poles in the closed unit disc \(\overline{\mathbb{D}}\).

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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsSaint Petersburg State UniversitySt. PetersburgRussia
  2. 2.ÉSPÉ d’Aix-MarseilleAix-Marseille UniversitéMarseille Cedex 04France

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