Dimension free bounds for the vector-valued Hardy-Littlewood maximal operator
Résumé
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.
Origine : Fichiers produits par l'(les) auteur(s)
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