Pointwise multiplication on vector-valued function spaces with power weights

Martin Meyries; Mark Veraar

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arXiv · 1311.7404

Pointwise multiplication on vector-valued function spaces with power weights

Martin Meyries·Mark Veraar

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Abstract

We investigate pointwise multipliers on vector-valued function spaces over $\mathbb{R}^d$, 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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Martin Meyries, Mark Veraar. 2014-08-28. Pointwise multiplication on vector-valued function spaces with power weights. https://arxiv.org/abs/1311.7404

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