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arXiv · 1607.02622

The H\"ormander multiplier theorem, II: The bilinear local $L^2$ case

Loukas Grafakos·Danqing He·Petr Honzík
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Abstract

We use wavelets of tensor product type to obtain the boundedness of bilinear multiplier operators on $\mathbb R^n\times \mathbb R^n$ associated with H\"ormander multipliers on $\mathbb R^{2n}$ with minimal smoothness. We focus on the local $L^2$ case and we obtain boundedness under the minimal smoothness assumption of $n/2$ derivatives. We also provide counterexamples to obtain necessary conditions for all sets of indices.

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Loukas Grafakos, Danqing He, Petr Honzík. 2016-07-09. The H\"ormander multiplier theorem, II: The bilinear local $L^2$ case. https://arxiv.org/abs/1607.02622

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