Multipliers of Hardy spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.30026
author: Zengjian Lou
author: Jidong Guo
publication date: 2002-07-28T00:00:00Z
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 1623633
zbMATH Keywords: Hardy spaces
zbMATH Keywords: Bloch space
MaRDI profile type: Publication
title: Multipliers of Hardy spaces
published in: Chinese Quarterly Journal of Mathematics
review text: Let \(X\) and \(Y\) be two vector spaces of sequences. A sequence \(\lambda= \{\lambda_n\}\) is said to be a multiplier from \(X\) to \(Y\), if \(\{\lambda_n x_n\}\in Y\) whenever \(\{x_n\}\in X\). The set of all multipliers from \(X\) to \(Y\) will be denoted by \((X,Y)\). We regard spaces of analytic functions in the open unit disc \(D\) as sequence space by identifying a function with its sequence of Taylor coefficients. \(H^p\), \(0<p\leq\infty\) denote the usual Hardy spaces on \(D\) and \(B\) denotes the Bloch space on \(D\). The author describes \((H^p,B)\) for \(1<p\leq \infty\) generalizing \((H^1,B)=B\). Moreover he shows (BMOA, \(H^q)=\ell^\infty\) for \(1\leq q\leq \infty\).
reviewed by: Takahiko Nakazi
description: scientific article; zbMATH DE number 1623633