Pointwise multiplication on vector-valued function spaces with power weights

2013/11/28 by Meyries, Martin, Veraar, Mark · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1311.7404

Abstract

We investigate pointwise multipliers on vector-valued function spaces over ℝ^d, equipped with Muckenhoupt weights. The main result is that in the natural parameter range, the characteristic function of the half-space is a pointwise multiplier on Bessel-potential spaces with values in a UMD Banach space. This is proved for a class of power weights, including the unweighted case, and extends the classical result of Shamir and Strichartz. The multiplication estimate is based on the paraproduct technique and a randomized Littlewood-Paley decomposition. An analogous result is obtained for Besov and Triebel-Lizorkin spaces.

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