Abstract
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 Schrödinger 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.
Citation
Koichi KAIZUKA. "Resolvent estimates on symmetric spaces of noncompact type." J. Math. Soc. Japan 66 (3) 895 - 926, July, 2014. https://doi.org/10.2969/jmsj/06630895
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