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.