We provide L1 estimates for a transport equation which contains singular integral operators. The form of the equation was motivated by the study of Kirchhoff-Sobolev parametrices in a Lorentzian space-time satisfying the Einstein equations. While our main application is for a specific problem in General Relativity we believe that the phenomenon which our result illustrates is of a more general interest.
All Science Journal Classification (ASJC) codes
- Applied Mathematics