English

A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$

Functional Analysis 2025-02-05 v1

Abstract

We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space Wk,1(Rd)W^{k,1}(\mathbb{R}^d) as the difference of two non-negative functions in the same space with control of their norms.

Keywords

Cite

@article{arxiv.1807.05221,
  title  = {A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$},
  author = {Augusto C. Ponce and Daniel Spector},
  journal= {arXiv preprint arXiv:1807.05221},
  year   = {2025}
}