Resolvent estimates on symmetric spaces of noncompact type
Resolvent estimates on symmetric spaces of noncompact type
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DOI：
10.2969/jmsj/06630895
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发表时间：
2014-07
影响因子：
0.7
通讯作者：
Koichi Kaizuka
中科院分区：
文献类型：
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作者：
Koichi Kaizuka
.本文证明了非紧型对称空间上的拉普拉斯- Beltrami算子或更一般的椭圆Fourier乘子的预解估计。然后Kato理论给出了相应色散方程的时间整体光滑估计，特别是Schr¨odinger发展方程。对于低频估计，伪维数表现为椭圆傅立叶乘子阶的上界。证明的关键是证明了修正的艾德Radon变换和分数次积分算子的加权L2连续性.
. In this article we prove resolvent estimates for the Laplace- Beltrami operator or more general elliptic Fourier multipliers on symmetric spaces of noncompact type. Then the Kato theory implies time-global smoothing estimates for corresponding dispersive equations, especially the Schr¨odinger evolution equation. For low-frequency estimates, a pseudo- dimension appears as an upper bound of the order of elliptic Fourier multipliers. A key of the proof is to show a weighted L 2 -continuity of the modified Radon transform and fractional integral operators.