An alternative proof of Tataru’s dispersive estimates. (English) Zbl 1539.35019
Summary: 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 \(\mathbb{H}^n\), 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, Trans. Am. Math. Soc. 353, No. 2, 795–807 (2001; Zbl 0956.35088)].
MSC:
| 35B45 | A priori estimates in context of PDEs |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35R01 | PDEs on manifolds |
| 46F10 | Operations with distributions and generalized functions |
| 58J45 | Hyperbolic equations on manifolds |
Citations:
Zbl 0956.35088References:
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