Lemmes de moyenne et Transformée aux rayons X Averaging Lemmas and the X-ray transform
نویسندگان
چکیده
We introduce a new method to prove averaging lemmas, i.e. prove a regularizing effect on the average in velocity of a solution to a kinetic equation. The method does not require the use of Fourier transform and the whole procedure is performed in the ’real space’; It leads to estimating an operator very similar to the so-called X-ray transform. We are then able to improve the known results when the integrability in space and velocity is different. Résumé. Nous introduisons une nouvelle méthode pour obtenir des lemmes de moyennes, c’est-à-dire prouver un effet régularisant pour les moyennes en vitesse d’une équation cinétique. Cette méthode ne fait pas appel à la transformée de Fourier et toute la preuve se fait dans “l’espace réel” ; on est alors ∗partially supported by the projects PICS 1014 and HPRN-CT-2002-00282
منابع مشابه
Lemmes De Moyenne Et Transform Ee Aux Rayons X Averaging Lemmas and the X-ray Transform on S'int Eresse a L' Equation Cin Etique Stationnaire Suivante
We introduce a new method to prove averaging lemmas, i.e. prove a regularizing eeect on the average in velocity of a solution to a kinetic equation. The method does not require the use of Fourier transform and the whole procedure is performed in the 'real space'; It leads to estimating an operator very similar to the so-called X-ray transform. We are then able to improve the known results when ...
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