Abstract
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 are different.
Translated title of the contribution | Averaging lemmas and the X-ray transform |
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Original language | French |
Pages (from-to) | 505-510 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 337 |
Issue number | 8 |
DOIs | |
State | Published - Oct 15 2003 |
All Science Journal Classification (ASJC) codes
- General Mathematics