Characteristic space-time estimates for the wave equation (Q5928275)

The operator \(Uf(x,t,\omega)=\square^{-1}(f(x)\cdot \delta (t-x\cdot \omega)),\) where \(\square^{-1}\) denotes the convolution with forward fundamental solution of the d'Alambertian on \(\mathbb{R}^{n+1},\) arises in the study of scattering by a potential on \(\mathbb{R}^{n}.\) The authors prove, that \(U\) is bounded as a mapping on locally supported and local variants of Sobolev and Besov spaces.