Interpolating sequences of complex hyperplanes in the unit ball of \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Interpolating sequences of complex hyperplanes in the unit ball of \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0565.32007
author: Pascal J. Thomas
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74722
review text: A sufficient condition is given to make a sequence \(L_ j\) of complex hyperplanes in the unit ball \(B^ n\subseteq {\mathbb{C}}^ n\) an interpolating sequence for \(H^{\infty}\), i.e. given holomorphic functions \(f_ j\) defined on each hyperplane of the sequence, \(\| f_ j\|_{\infty}\leq 1\), there exists a function \(f\in H^{\infty}(B^ n)\) such that \(f|_{L_ j}=f_ j.\) Comparisons are made with results concerning interpolating sequences of points; the exponent in Varopoulos' necessary condition for interpolating sequences of points is shown to be sharp even for sequences of hyperplanes.
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32E30
zbMATH DE Number: 3901150
zbMATH Keywords: Carleson measures
zbMATH Keywords: unit ball
zbMATH Keywords: interpolating sequence for \(H^{\infty }\)
zbMATH Keywords: sequences of hyperplanes
MaRDI profile type: Publication
OpenAlex ID: W1970510316
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DOI: 10.5802/AIF.1064
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 3901150