Universal classes of Orlicz function spaces

Francisco Luis Hernández Rodríguez and Cesar Ruiz

Vol. 155 (1992), No. 1, 87–98

DOI: 10.2140/pjm.1992.155.87

Abstract

It is shown that for each 0 < p < q < ∞ the space L^p(0,∞) + L^q(0,∞), defined as in Interpellation Theory, is universal for the class of all Orlicz function spaces L^ψ with Boyd indices strictly between p and q (i.e. every Orlicz function space L^ψ is order-isomorphically embedded into L^p(0,∞) + L^q(0,∞)). The extreme case of spaces having Boyd indices equal to p or q is also studied. In particular every space L^r(0,∞) + L^s(0,∞) embeds isomorphically into the sum L^p(0,∞) + L^q(0,∞) for any 0 < p ≤ r ≤ s < q < ∞.

Mathematical Subject Classification 2000

Primary: 46E30

Milestones

Received: 18 May 1990

Published: 1 September 1992