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

2014/07/23 by Anton Baranov, Rachid Zarouf, Baranov, Anton +1
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1407.6347

openalex publication_date 2014/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an inner function Θ in the unit disc \mathbbD, we study the boundedness of the differentiation operator which acts from from the model subspace K_Θ=(ΘH²)^⊥ of the Hardy space H², 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≥1 having no poles in the closed unit disc \mathbbD.

Citations

• On Analytic Functions of Bounded Mean Oscillation

Related

• Volterra type integration operators from Bergman spaces to Hardy spaces
• Idempotent, model, and Toeplitz operators attaining their norms
• Weighted norm inequalities for de Branges--Rovnyak spaces and their applications
• A model space approach to some classical inequalities for rational functions
• Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators