English

A Characterization of $\mathcal{M}_{A_1}(\mathbb{R}^n)$

Classical Analysis and ODEs 2013-10-09 v1

Abstract

We characterize the set of all measurable functions on \RRn\RR^n possessing an A1A_1 majorant, denoted as \cMA1(\RRn)\cM_{A_1}(\RR^n), by certain Banach function spaces. We prove that a function has an A1A_1 majorant if and only if it belongs to some Banach function space for which the Hardy-Littlewood maximal operator is bounded. This answers the question posted by G. Knese, J. Mc^{c}Carthy, and K. Moen.

Keywords

Cite

@article{arxiv.1310.2136,
  title  = {A Characterization of $\mathcal{M}_{A_1}(\mathbb{R}^n)$},
  author = {Cheng Chu},
  journal= {arXiv preprint arXiv:1310.2136},
  year   = {2013}
}
R2 v1 2026-06-22T01:42:32.801Z