The Hörmander multiplier theorem, II: The bilinear local $L^2$ case

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 Hörmander 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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