Affiliation:
1. School of Mathematical Sciences , Zhejiang University , Hangzhou 310058 , P. R. China
Abstract
Abstract
The aim of this article is to give an alternative proof of Tataru’s dispersive estimates for wave equations posed on the hyperbolic space. Based on the formula for the wave kernel on
ℍ
n
{\mathbb{H}^{n}}
,
we give the proof from the perspective of Bessel potentials, by
exploiting various facts about Gamma functions, modified Bessel functions, and Bessel potentials.
This leads to our proof being more self-contained than that in
[D. Tataru,
Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation,
Trans. Amer. Math. Soc. 353 2001, 2, 795–807].
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,General Mathematics
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