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