Composition property of holomorphic functions on the ball
type: Item
instance of: scholarly article
title: Composition property of holomorphic functions on the ball
zbMATH Open document ID: 0693.32005
author: Boo Rim Choe
published in: Michigan Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let \(\phi\) be a homogeneous polynomial in \({\mathbb{C}}^ n\) such that \(\phi (B_ n)=B_ 1\) (here \(B_ k=\{z\in {\mathbb{C}}^ k:\) \(\| z\| <1\})\) and let g be a Bloch function in \(B_ 1.\) The author proves that \(g\circ \phi\) is in \(H^ p(B_ n)\) for every \(p\in (0,\infty)\). Moreover, if \(\phi\) is a homogeneous polynomial, then, as it is shown, one may find such an exponent \(\alpha =\alpha (\phi)\leq n-2\) that \(h\circ \phi \in H^ p(B_ n)\) for every \(p\in (0,\infty)\) and every \(h\in A(B_ 1)\) with the property \(\int_{B_ 1}| h|^ p(1-| z|^ 2)^{\alpha}dm<\infty.\)
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32A10
zbMATH DE Number: 4134430
zbMATH Keywords: homogeneous polynomial
zbMATH Keywords: Bloch function
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003950
OpenAlex ID: W1981496441
DOI: 10.1307/MMJ/1029003950
description: scientific article; zbMATH DE number 4134430