Note on Order-Isomorphic Isometric Embeddings of Some Recent Function Spaces

Abstract

We investigate certain recently introduced ODE-determined varying exponent Lp spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent lp space. Moreover, this can be accomplished in a natural unified fashion. This leads to order-isomorphic isometric embeddings of all of the above Lp spaces to an ultrapower of the above varying exponent lp space.