Resumen de Sharp L1 estimates for singular transport equations

Sergiu Klainerman, Igor Rodnianski

• 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 verifying 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.