JournalsjemsVol. 10 , No. 2DOI 10.4171/jems/119

Sharp <em>L</em><sup>1</sup> estimates for singular transport equations

  • Sergiu Klainerman

    Princeton University, USA
  • Igor Rodnianski

    Massachusetts Institute of Technology, Cambridge, USA
Sharp <em>L</em><sup>1</sup> estimates for singular transport equations cover

Abstract

We provide _L_1 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.