Note on order-isomorphic isometric embeddings of some recent function spaces

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