Revista Matemática Iberoamericana


Full-Text PDF (328 KB) | Metadata | Table of Contents | RMI summary
Volume 35, Issue 1, 2019, pp. 101–123
DOI: 10.4171/rmi/1050

Published online: 2019-01-04

Dimension free bounds for the vector-valued Hardy–Littlewood maximal operator

Luc Deleaval[1] and Christoph Kriegler[2]

(1) Université Paris-Est Marne-la-Vallée, France
(2) Université Clermont Auvergne, Aubière, France

In this article, Fefferman–Stein inequalities in $L^p(\mathbb R^d; \ell^q)$ with bounds independent of the dimension $d$ are proved, for all $1 < p,q < +\infty$. This result generalizes in a vector-valued setting the famous one by Stein for the standard Hardy–Littlewood maximal operator. We then extend our result by replacing $\ell^q$ with an arbitrary UMD Banach lattice. Finally, we prove similar dimensionless inequalities in the setting of the Grushin operators.

Keywords: Hardy–Littlewood maximal operator, dimension free bounds, vector-valued estimates, UMD Banach lattice, Grushin operator

Deleaval Luc, Kriegler Christoph: Dimension free bounds for the vector-valued Hardy–Littlewood maximal operator. Rev. Mat. Iberoam. 35 (2019), 101-123. doi: 10.4171/rmi/1050