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Dimension free bounds for the vector-valued Hardy-Littlewood maximal operator (1703.08327v1)

Published 24 Mar 2017 in math.FA and math.CA

Abstract: In this article, Fefferman-Stein inequalities in $Lp(\mathbb Rd;\ellq)$ withbounds independent of the dimension $d$ are proved, for all $1 \textless{} p, q \textless{} + \infty.$This result generalizes in a vector-valued setting the famous one by Steinfor the standard Hardy-Littlewood maximal operator. We then extendour result by replacing $\ellq$ with an arbitrary UMD Banach lattice. Finally,we prove similar dimensionless inequalities in the setting of the Grushinoperators.

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