English

On the structure of variable exponent spaces

Functional Analysis 2025-05-29 v1

Abstract

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

Keywords

Cite

@article{arxiv.1911.03613,
  title  = {On the structure of variable exponent spaces},
  author = {Julio Flores and Francisco L. Hernández and César Ruiz and Mauro Sanchiz},
  journal= {arXiv preprint arXiv:1911.03613},
  year   = {2025}
}
R2 v1 2026-06-23T12:10:03.827Z