Duality of ODE-determined norms

TL;DR

This paper investigates the duality properties of ODE-determined variable exponent $L^{p(ullet)}$ spaces, characterizing superreflexivity and providing a universal space construction, advancing the theoretical understanding of these novel function spaces.

Contribution

The paper analyzes the duality of ODE-determined $L^{p(ullet)}$ spaces, characterizes their superreflexivity, and introduces a universal space construction, expanding the theoretical framework.

Findings

Duality of ODE-determined $L^{p(ullet)}$ spaces is established.

Superreflexivity is characterized under certain conditions.

A universal space construction for these spaces is provided.

Abstract

Recently a new approach to varying exponent $L^{p(\cdot)}$ space norms employing weak solutions to first order ordinary differential equations was initiated by the author. The duality of these ODE-determined $L^{p(\cdot)}$ spaces is analyzed here. The superreflexivity of these spaces is characterized under the anticipated conditions. A universal space construction is also given for these spaces.