Comptes Rendus
no. 6
Partial differential equations/Harmonic analysis
Fractional Laplacians, extension problems and Lie groups

Presented by: Haïm Brézis

Diego Chamorro1; Oscar Jarrín1
1 Laboratoire de mathématiques et modélisation d'Évry (LaMME), UMR 8071, Université d'Évry-Val-d'Essonne, 23, boulevard de France, 91037 Évry cedex, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 517-522.

We generalize some results concerning the fractional powers of the Laplace operator to the setting of nilpotent Lie Groups and we study its relationship with the solutions to a partial differential equation in the spirit of the articles of Caffarelli & Silvestre [1] and Stinga & Torrea [7].

Nous généralisons aux groupes de Lie nilpotents les travaux de Caffarelli & Silvestre [1] et Stinga & Torrea [7] concernant la relation existant entre les puissances fractionnaires de l'opérateur laplacien et les solutions d'une équation aux dérivées partielles.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.04.007

Diego Chamorro 1; Oscar Jarrín 1

1 Laboratoire de mathématiques et modélisation d'Évry (LaMME), UMR 8071, Université d'Évry-Val-d'Essonne, 23, boulevard de France, 91037 Évry cedex, France 
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Diego Chamorro; Oscar Jarrín. Fractional Laplacians, extension problems and Lie groups. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 517-522. doi : 10.1016/j.crma.2015.04.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.007/

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[3] R. Frank; M.D.M. González; D.D. Monticelli; J. Tan An extension problem for the CR fractional Laplacian, Adv. Math., Volume 270 (2015), pp. 97-137

[4] G. Furioli; C. Melzi; A. Veneruso Littlewood–Paley decomposition and Besov spaces on Lie groups of polynomial growth, Math. Nachr., Volume 279 (2006) no. 9–10, pp. 1028-1040

[5] J.E. Galé; P.J. Miana; P.R. Stinga Extension problems and fractional operators: semi-groups and wave equations | arXiv

[6] M. Kemmppainen; S. Sjögren; J.L. Torrea Wave extension problem for the fractional Laplacian, J. Evol. Equ., Volume 2 (2014), pp. 343-368

[7] P. Stinga; J. Torrea Extension problem and Harnack's inequality for some fractional operators, Commun. Partial Differ. Equ., Volume 35 (2010) no. 11, pp. 2092-2122

[8] N.T. Varopoulos; L. Saloff-Coste; T. Coulhon Analysis and Geometry on Groups, Cambridge Tracts in Mathematics, vol. 100, 1992

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