Geodesic
An Application of Homogenization Theory to Harmonic Analysis: Harnack Inequalities And Riesz Transforms on Lie Groups of Polynomial Growth
Canadian journal of mathematics, Tome 44 (1992) no. 4, pp. 691-727

Voir la notice de l'article provenant de la source Cambridge University Press

We prove a homogenization formula for a sub-Laplacian are left invariant Hörmander vector fields) on a connected Lie group Gof polynomial growth. Then using a rescaling argument inspired from M. Avellanedaand F. H. Lin [2], we prove Harnack inequalities for the positive solutions of the equation (∂/∂t+ L)u= 0. Using these inequalities and further exploiting the algebraic structure of Gwe prove that the Riesz transforms , are bounded on Lq,1 < q <+∞ and from L1 to weak-L1.
DOI : 10.4153/CJM-1992-042-x
Mots-clés : 22E15, 22E30, 43E80, Homogenization, Lie groups, volume growth, Harnack inequalities, Riesz transforms 
Alexopoulos, G. An Application of Homogenization Theory to Harmonic Analysis: Harnack Inequalities And Riesz Transforms on Lie Groups of Polynomial Growth. Canadian journal of mathematics, Tome 44 (1992) no. 4, pp. 691-727. doi: 10.4153/CJM-1992-042-x
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