JournalsjemsVol. 10, No. 2pp. 477–505

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
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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.

Cite this article

Sergiu Klainerman, Igor Rodnianski, Sharp <em>L</em><sup>1</sup> estimates for singular transport equations. J. Eur. Math. Soc. 10 (2008), no. 2, pp. 477–505

DOI 10.4171/JEMS/119