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EnglishLet X = G/K be a symmetric space of noncompact type, L be the Laplace-Beltrami operator on X, and b the bottom of its spectrum. In this paper we study the behaviour of the Lp-Lq operator norms of the (σ,θ)-Poisson semigroup as t tends to zero and to infinity for all such p and q. As t tends to infinity the behaviour of these norms involves power of t in which the rank (r) and the pseudo-dimension of X play an important role. Two features of our study are noteworthy. First, while the θ-heat semigroup is Lp-Lq bounded whenever 1≤p≤q≤∞, the (σ,θ)-Poisson semigroup is not Lp-Lq bounded for many such p and q. Second, when p and q reach the critical index for Lp-Lq boundedness, the exponent r+1 appears.
Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II / M. COWLING; S. GIULINI; S. MEDA. - In: JOURNAL OF LIE THEORY. - ISSN 0949-5932. - STAMPA. - 5(1995), pp. 1-11.
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| Titolo: | Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II | |
| Autori: | ||
| Data di pubblicazione: | 1995 | |
| Rivista: | ||
| Citazione: | Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II / M. COWLING; S. GIULINI; S. MEDA. - In: JOURNAL OF LIE THEORY. - ISSN 0949-5932. - STAMPA. - 5(1995), pp. 1-11. | |
| Abstract: | Let X = G/K be a symmetric space of noncompact type, L be the Laplace-Beltrami operator on X, and b the bottom of its spectrum. In this paper we study the behaviour of the Lp-Lq operator norms of the (σ,θ)-Poisson semigroup as t tends to zero and to infinity for all such p and q. As t tends to infinity the behaviour of these norms involves power of t in which the rank (r) and the pseudo-dimension of X play an important role. Two features of our study are noteworthy. First, while the θ-heat semigroup is Lp-Lq bounded whenever 1≤p≤q≤∞, the (σ,θ)-Poisson semigroup is not Lp-Lq bounded for many such p and q. Second, when p and q reach the critical index for Lp-Lq boundedness, the exponent r+1 appears. | |
| Handle: | http://hdl.handle.net/11567/187472 | |
| Appare nelle tipologie: | 01.01 - Articolo su rivista |
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