A maximum principle for the Bergman space
type: Item
instance of: scholarly article
title: A maximum principle for the Bergman space
zbMATH Open document ID: 0758.30020
DOI: 10.5565/PUBLMAT_35291_12
author: Boris Korenblum
published in: Publicacions Matemàtiques
publication date: 1992-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/41707
review text: Let \(f\), \(g\) be analytic in the unit disk \(\mathbb{D}\), and let \(f\) have a zero of order \(\geq k\) in \(\zeta\in\mathbb{D}\) if \(g\) has a zero of order \(k\) in \(\zeta\). The author proves, that \(| f(z)|\geq| g(z)|\) for \({1\over2}e^{-2}<| z|<1\) implies the inequality \[ \int_ \mathbb{D} | g(z)|^ 2 dm\leq\int_ \mathbb{D} | f(z)|^ 2 dm, \] where \(m\) is the Lebesgue measure.
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 31630
zbMATH Keywords: maximumprinciple
zbMATH Keywords: zero
zbMATH Keywords: Lebesgue measure
reviewed by: Klaus Menke
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 31630