English

The Muckenhoupt condition

Functional Analysis 2025-09-16 v3 Classical Analysis and ODEs

Abstract

The goal of this paper is to unify the theory of weights beyond the setting of weighted Lebesgue spaces in the general setting of quasi-Banach function spaces. We prove new characterizations for the boundedness of singular integrals, pose several conjectures, and prove partial results related to the duality of the Hardy-Littlewood maximal operator. Furthermore, we give an overview of the theory applied to weighted variable Lebesgue, Morrey, and Musielak-Orlicz spaces.

Keywords

Cite

@article{arxiv.2405.20907,
  title  = {The Muckenhoupt condition},
  author = {Zoe Nieraeth},
  journal= {arXiv preprint arXiv:2405.20907},
  year   = {2025}
}

Comments

46 pages, final version, accepted for publication in J. Funct. Anal

R2 v1 2026-06-28T16:48:33.790Z