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Sharp L 1 estimates for singular transport equations

Sergiu Klainerman, Igor Rodnianski (2008)

Journal of the European Mathematical Society

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 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.

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