Convolutions of singular measures and applications to the Zakharov system

Uniform L2-estimates for the convolution of singular measures with respect to transversal submanifolds are proved in arbitrary space dimension. The results of Bennett–Bez are used to extend previous work of Bejenaru–Herr–Tataru. As an application, it is shown that the 3D Zakharov system is locally well-posed in the full subcritical regime. © 2011 Elsevier Inc. All rights reserved.