English

Recovering functions via doubly homogeneous nonlocal gradients

Functional Analysis 2025-11-04 v1 Analysis of PDEs

Abstract

We investigate a class of nonlocal gradients featuring distinct homogeneities at zero and infinity. We establish a representation formula for such doubly homogeneous operators and derive associated Sobolev-type inequalities. We also propose open questions linked to our results, suggesting directions for future research inspired by the work of Haim Brezis.

Keywords

Cite

@article{arxiv.2511.01606,
  title  = {Recovering functions via doubly homogeneous nonlocal gradients},
  author = {Stefano Buccheri and Augusto C. Ponce},
  journal= {arXiv preprint arXiv:2511.01606},
  year   = {2025}
}

Comments

Dedicated to the memory of Haim Brezis, with deep admiration and gratitude