Analyse sur les groupes de Lie à croissance polynômiale. (Analysis on Lie groups of polynomial growth)
Let G be a connected real Lie group with the property that there is a positive integer D such that for any symmetric compact neighborhood \(\Omega\) of the unit element in G, we have \(| \Omega^ n| \cong n^ D\) for \(n=1,2,...\), where \(| \Omega |\) is the volume of \(\Omega\) in G. For instance nilpotent Lie groups have the property above. For analysis on G the following is investigated: the Lipschitz space, the Sobolev theorem, the inequality of Trudinger, the Hardy space \(H^ 1\), the Riesz transform, and the Harnack theorem. Sharp estimates for the heat kernel on G are used in this analysis.
scientific article; zbMATH DE number 4177853
scientific article