L p -L q estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III  [ Estimations L p -L q de fonctions de l’opérateur de Laplace-Beltrami pour les espaces symétriques non compacts. III ]
Annales de l'Institut Fourier, Tome 51 (2001) no. 4, p. 1047-1069
Soit X un espace symétrique du type noncompact, soit - son opérateur Laplace- -Beltrami, et soit [b,) le spectre de (vu comme opérateur sur L 2 (X)). Si τ et Re τ0, notons 𝒫 τ l’opérateur exp (-τ(-b) 1/2 ) sur L 2 (X). On démontre des estimations de la norme de 𝒫 τ de L p dans L q pour chaque τ, qui sont optimales si |τ|T ou | arg τ|φ<π/2.
Let X be a symmetric space of the noncompact type, with Laplace–Beltrami operator -, and let [b,) be the L 2 (X)-spectrum of . For τ in such that Re τ0, let 𝒫 τ be the operator on L 2 (X) defined formally as exp (-τ(-b) 1/2 ). In this paper, we obtain L p -L q operator norm estimates for 𝒫 τ for all τ, and show that these are optimal when τ is small and when | arg τ| is bounded below π/2.
DOI : https://doi.org/10.5802/aif.1844
Classification:  22E46,  22E30,  58J35,  58J45
Mots clés: Espace symétrique, équation des ondes, estimations L p -L q
@article{AIF_2001__51_4_1047_0,
     author = {Cowling, Michael and Giulini, Saverio and Meda, Stefano},
     title = {$L^p-L^q$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {4},
     year = {2001},
     pages = {1047-1069},
     doi = {10.5802/aif.1844},
     zbl = {0980.43007},
     mrnumber = {1849214},
     language = {en},
     url = {http://http://www.numdam.org/item/AIF_2001__51_4_1047_0}
}
Cowling, Michael; Giulini, Saverio; Meda, Stefano. $L^p-L^q$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III. Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1047-1069. doi : 10.5802/aif.1844. http://www.numdam.org/item/AIF_2001__51_4_1047_0/

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