Universal classes of Orlicz function spaces
type: Item
instance of: scholarly article
title: Universal classes of Orlicz function spaces
zbMATH Open document ID: 0731.46010
author: Francisco L. Hernández
author: César Ruiz
published in: Pacific Journal of Mathematics
publication date: 1992-01-01T00:00:00Z
review text: It is proved that for each \(0<p<q<\infty\), the space \(L^ p(0,\infty)+L^ q(0,\infty)\), defined as in interpolation theory, is universal for the class of all Orlicz function spaces \(L^{\psi}\) with Boyd indices strictly between p and q (i.e. every Orlicz function space \(L^{\psi}\) is order-isomorphically embedded into \(L^ p(0,\infty)+L^ q(0,\infty))\). The extreme case of spaces having Boyd indices equal to p or q is also studied. In particular every space \(L^ r(0,\infty)+L^ q(0,\infty)\) embeds isomorphically into the sum \(L^ p(0,\infty)+L^ q(0,\infty)\) for any \(0<p\leq r\leq s<q<\infty\). The case \(p=r=2\) has been proved before by \textit{S. Dilwoth} using a different argument [Ill. J. Math. 34, 140-158 (1990; Zbl 0693.46024)].
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 4208823
zbMATH Keywords: interpolation theory
zbMATH Keywords: Orlicz function spaces
zbMATH Keywords: Boyd indices
MaRDI profile type: Publication
full work available at URL: pjm.1992.155.87
OpenAlex ID: W1999478045
DOI: 10.2140/PJM.1992.155.87
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description: scientific article; zbMATH DE number 4208823