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

Abstract

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.
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Dates and versions

hal-01494518 , version 1 (23-03-2017)

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Luc Deleaval, Christoph Kriegler. Dimension free bounds for the vector-valued Hardy-Littlewood maximal operator. 2017. ⟨hal-01494518⟩
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