Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, an...Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.展开更多
The author studies the oscillating multipliers on Riemannian symmetric spaceSL(3,IH)/Sp(3).The results are analogous to that for Riemannian symmetric spaces of rank one and of complex type.
Let G/K be the noncompact Riemannian symmetric space SL(3, H)/Sp(3). We shall prove in this paper that for f∈L^P(SL(3, H)/Sp(3)), 1≤p≤2. the Riesz means of order z of f with respect to the eigenfunctions expansion ...Let G/K be the noncompact Riemannian symmetric space SL(3, H)/Sp(3). We shall prove in this paper that for f∈L^P(SL(3, H)/Sp(3)), 1≤p≤2. the Riesz means of order z of f with respect to the eigenfunctions expansion of Laplace operator almost everywhere converge to f for Rez】б(n, p). The critical index δ(n,p) is the same as in the classical Stein’s result for Euclidean space. and as in the noncompact symmetric spaces of rank one and of complex type.展开更多
文摘Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.
文摘The author studies the oscillating multipliers on Riemannian symmetric spaceSL(3,IH)/Sp(3).The results are analogous to that for Riemannian symmetric spaces of rank one and of complex type.
基金Partially supported by National Natural Science Foundation of China
文摘Let G/K be the noncompact Riemannian symmetric space SL(3, H)/Sp(3). We shall prove in this paper that for f∈L^P(SL(3, H)/Sp(3)), 1≤p≤2. the Riesz means of order z of f with respect to the eigenfunctions expansion of Laplace operator almost everywhere converge to f for Rez】б(n, p). The critical index δ(n,p) is the same as in the classical Stein’s result for Euclidean space. and as in the noncompact symmetric spaces of rank one and of complex type.
