English

On off-diagonal operators in matrix-weighted spaces

Classical Analysis and ODEs 2026-07-20 v1 Functional Analysis

Abstract

In this paper we prove matrix-weighted inequalities for fractional operators and their commutators. We do so by developing the theory of convex body domination for such operators. Using this approach we prove quantitative estimates for the fractional integral operator (or Riesz potential) and its commutators, and prove matrix-weighted Gagliardo-Nirenberg-Sobolev inequalities for vector-valued functions.

Cite

@article{arxiv.2607.18175,
  title  = {On off-diagonal operators in matrix-weighted spaces},
  author = {David Cruz-Uribe and Aapo Laukkarinen and Kabe Moen},
  journal= {arXiv preprint arXiv:2607.18175},
  year   = {2026}
}