Duality and multipliers for mixed norm spaces
type: Item
instance of: scholarly article
title: Duality and multipliers for mixed norm spaces
zbMATH Open document ID: 0538.30039
author: Patrick Ahern
author: Miroljub Jevtić
published in: Michigan Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: In the paper the authors consider a number of questions concerning duality and multipliers for the spaces \(A^{p,q,\alpha}\), where for \(p>0,\quad q>0,\quad \alpha<-1, A^{p,q,\alpha}\) denotes the space of functions f, holomorphic in the unit disc, for which \[ \int^{1}_{0}(1-r)^{\alpha}M_ q(r,f)^ pdr<\infty,\quad where \] \[ M_ q(r,f)^ q=(1/2\pi)\int^{2\pi}_{0}| f(re^{i\theta})|^ qd\theta, \] with the usual understanding if p or \(q=\infty.\) In the first section, the authors deal with the dual space of \(A^{p,q,\alpha}\), listing some known results and calculating the dual for the cases \(q=1\), \(1<p<\infty,\) and \(q=\infty, 1<p<\infty.\) In the second section, they use the duality results of the first section along with a method of \textit{J. M. Anderson} and \textit{A. L. Shields} [Trans. Am. Math. Soc. 224, 255-265 (1976; Zbl 0352.30032)] to calculate the coefficient multipliers of some of the spaces \(A^{p,q,\alpha}\). In the final section, the authors introduce some special mixed norm spaces \(D^{p,q}\) and give a number of results for these spaces, including results on duality, multipliers, and fractional derivatives.
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 3855462
zbMATH Keywords: multipliers
zbMATH Keywords: fractional derivatives
reviewed by: Manfred Stoll
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029002787
OpenAlex ID: W2067840313
DOI: 10.1307/MMJ/1029002787
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description: scientific article; zbMATH DE number 3855462