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Theses

Inégalités de Gagliardo-Nirenberg précisées sur le groupe de Heisenberg

Abstract : This thesis studies the generalization of improved Gagliardo Nirenberg inequalities on stratified Lie groups. In the Euclidian case there are three methods according to the value of p, who characterizes the space of Sobolev. The first series of this inequalities concerns the case p> 1. The demonstration of these estimations follows directly from the characterization of the functional spaces with a Littlewood Paley analysis. To handle the case p=1, we use the properties of the heat kernel by generalizing the pseudo inequality of Poincaré. This case also allows the study of the space of the fonctions of bounded variation BV. But this method does not allow us to consider a space of Sobolev in the left member of the inequality. The third method of demonstration relies on a decomposition with wavelettes. The generalization of this result to the Heisenberg group remains opened.
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Submitted on : Tuesday, February 20, 2007 - 2:01:00 PM
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  • HAL Id : tel-00132135, version 1

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Diego Chamorro. Inégalités de Gagliardo-Nirenberg précisées sur le groupe de Heisenberg. Mathématiques [math]. École normale supérieure de Cachan - ENS Cachan, 2006. Français. ⟨tel-00132135⟩

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