Soit un sous-Laplacien invariant à droite sur un groupe de Lie et soit l’opérateur “sommes sphériques partielles” associé, où dénote la résolution spectrale de Nous prouvons que converge vers p.p. quand si
Let be a right-invariant sub-Laplacian on a connected Lie group and let denote the associated “spherical partial sums,” where is the spectral resolution of We prove that converges a.e. to as under the assumption
@article{AIF_2007__57_5_1509_0, author = {Meaney, Christopher and M\"uller, Detlef and Prestini, Elena}, title = {A.e. convergence of spectral sums on Lie groups}, journal = {Annales de l'Institut Fourier}, volume = {57}, year = {2007}, pages = {1509-1520}, doi = {10.5802/aif.2303}, zbl = {1131.22007}, mrnumber = {2364139}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_2007__57_5_1509_0} }
Meaney, Christopher; Müller, Detlef; Prestini, Elena. A.e. convergence of spectral sums on Lie groups. Annales de l'Institut Fourier, Tome 57 (2007) pp. 1509-1520. doi : 10.5802/aif.2303. http://gdmltest.u-ga.fr/item/AIF_2007__57_5_1509_0/
[1] Convergence Problems of Orthogonal Series., Pergamon Press, Oxford, New York, International Series of Monographs in Pure and Applied Mathematics, Tome 20 (1961) (Translated from the German by I. Földer) | MR 218827 | Zbl 0098.27403
[2] Almost-Everywhere Convergence of Fourier Integrals for Functions in Sobolev Spaces, and an -Localisation Principle, Rev. Mat. Iberoamericana, Tome 4 (1988) no. 2, pp. 319-337 | MR 1028744 | Zbl 0692.42001
[3] bounds for spectral multipliers on nilpotent groups., Trans. Amer. Math. Soc., Tome 328 (1991) no. 1, pp. 73-81 | Article | MR 1104196 | Zbl 0739.42010
[4] Almost everywhere convergence of inverse Fourier transforms., Proc. Amer. Math. Soc., Tome 134 (2006) no. 6, pp. 1651-1660 | Article | MR 2204276 | Zbl 1082.42006
[5] Hardy Spaces on Homogeneous Groups, Princeton University Press, Princeton, N.J., Mathematical Notes, Tome 28 (1982) | MR 657581 | Zbl 0508.42025
[6] Almost everywhere summability on nilmanifolds, Trans. Amer. Math. Soc., Tome 278 (1983) no. 2, pp. 703-715 | Article | MR 701519 | Zbl 0516.43010
[7] Sub-Laplacians of holomorphic -type on rank one -groups and related solvable groups, J. Funct. Anal., Tome 170 (2000) no. 2, pp. 366-427 | Article | MR 1740657 | Zbl 0957.22013
[8] Analysis and Geometry on Groups, Cambridge University Press, Cambridge, Cambridge Tracts in Mathematics, Tome 100 (1992) | MR 1218884 | Zbl 0813.22003
[9] Trigonometric Series, Cambridge Mathematical Library. Cambridge University Press, Cambridge Tome 1 and 2 (2002) (With a foreword by Robert A. Fefferman) | MR 1963498 | Zbl 1084.42003