Bilinear space-time estimates for homogeneous wave equations

In this paper, we pursue a systematic treatment of the regularity theory for products and bilinear forms of solutions of the homogeneous wave equation. We discuss necessary and sufficient conditions for the validity of bilinear estimates, based on L-2 norms in space and time, of derivatives of products of solutions. Also, we give necessary conditions and formulate some conjectures for similar estimates based on (LtLxr)-L-q, norms. (C) 2000 Editions scientifiques et medicales Elsevier SAS.