On the structure of variable exponent spaces

Abstract

The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) $\lpv$. In the second part strictly singular and disjointly strictly singular operators between spaces $\lpv$ are studied. New results on the disjoint strict singularity of the inclusions $L^{p(\cdot )}(\Omega )\hookrightarrow L^{q(\cdot )}(\Omega )$ are given.