On interpolation in the classes \(E^p\)
type: Item
instance of: scholarly article
title: On interpolation in the classes \(E^p\)
zbMATH Open document ID: 0974.30030
DOI: 10.1007/BF02676450
author: D. Ya. Danchenko
published in: Mathematical Notes
publication date: 2001-04-01T00:00:00Z
review text: Consider a Jordan domain \(G\) in the (extended) complex plane and a sequence \(\lambda= (z_j)\) in \(G\). For \(1<p< \infty\) the author studies interpolation problems of the form (1) \(\rho_j^{1/p} f(z_j)=a_j\) \((u\in \mathbb{N})\) where \((a_j)\) is an arbitrary sequence of complex numbers with \(|a_j|\leq 1\) and \(\rho_j= \text{dist}(z_j, \partial G)\), and where the interpolating functions belong to the Smirnov class \(E^p\) in \(G\). For a certain class of Jordan domains (so-called Ahlfors class) and for a certain class of sequences \(\lambda\) he shows that (1) is solvable for all \((a_j)\) as above with a function \(f\in E^p\) in such a way that the \(E^p\) norm of \(f\) is bounded by some constant depending on \(G,\lambda,p\) and some sequence of weights.
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 1467839
zbMATH Keywords: moment problem
zbMATH Keywords: Jordan domain
zbMATH Keywords: interpolation problems
zbMATH Keywords: Smirnov class
zbMATH Keywords: Ahlfors class
reviewed by: Jürgen Müller
MaRDI profile type: Publication
cites work: On Some Interpolation Problems for Analytic Functions
cites work: Q3922907
cites work: Q3874458
full work available at URL: https://doi.org/10.1007/bf02676450
OpenAlex ID: W2066909812
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description: scientific article; zbMATH DE number 1467839