Geodesic
Sharp $L^1$ estimates for singular transport equations
Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 477-505

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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.
DOI : 10.4171/jems/119
Classification : 35-XX, 00-XX, 76-XX 
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     author = {Sergiu Klainerman and Igor Rodnianski},
     title = {Sharp $L^1$ estimates for singular transport equations},
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     pages = {477--505},
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     year = {2008},
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Sergiu Klainerman; Igor Rodnianski. Sharp $L^1$ estimates for singular transport equations. Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 477-505. doi: 10.4171/jems/119

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