Dimension free bounds for the vector-valued Hardy–Littlewood maximal operator
Luc Deleaval
Université Paris-Est Marne-la-Vallée, FranceChristoph Kriegler
Université Clermont Auvergne, Aubière, France
![Dimension free bounds for the vector-valued Hardy–Littlewood maximal operator cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-35-issue-1.png&w=3840&q=90)
Abstract
In this article, Fefferman–Stein inequalities in with bounds independent of the dimension are proved, for all . 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 with an arbitrary UMD Banach lattice. Finally, we prove similar dimensionless inequalities in the setting of the Grushin operators.
Cite this article
Luc Deleaval, Christoph Kriegler, Dimension free bounds for the vector-valued Hardy–Littlewood maximal operator. Rev. Mat. Iberoam. 35 (2019), no. 1, pp. 101–123
DOI 10.4171/RMI/1050