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

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 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.

14 pages