English

Characterization of generalized Orlicz spaces

Functional Analysis 2020-08-06 v1

Abstract

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz-Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

Keywords

Cite

@article{arxiv.1612.04566,
  title  = {Characterization of generalized Orlicz spaces},
  author = {Rita Ferreira and Peter Hästö and Ana Margarida Ribeiro},
  journal= {arXiv preprint arXiv:1612.04566},
  year   = {2020}
}

Comments

18 pages

R2 v1 2026-06-22T17:23:22.493Z