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December  2008, 1(4): 491-513. doi: 10.3934/krm.2008.1.491

Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$

Radjesvarane Alexandre 1, and  Lingbing He 2,

1. 

IRENAV, French Naval Academy, 29240 BREST ARMEES, France
2. 

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  June 2008 Revised  June 2008 Published  October 2008

In this work, we show that integral estimates for a linear operator linked with Boltzmann quadratic operator considered in [1] can also be obtained for the case of higher singularities. Some estimates proven in this earlier work are improved, as in particular, we do not need any regularity with respect to the first function.
Keywords: Boltzmann operator, non cut off kernels, harmonic analysis.
Mathematics Subject Classification: Primary: 42B25, 35Sxx; Secondary: 35Qxx.
Citation: Radjesvarane Alexandre, Lingbing He. Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$. Kinetic and Related Models, 2008, 1 (4) : 491-513. doi: 10.3934/krm.2008.1.491
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