Universal classes of Orlicz function spaces
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)].
scientific article; zbMATH DE number 4208823