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 possessing an majorant, denoted as , by certain Banach function spaces. We prove that a function has an 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. MCarthy, 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}
}