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# Mathematical Research Letters

## Volume 21 (2014)

### Number 6

### Non-trapping estimates near normally hyperbolic trapping

Pages: 1277 – 1304

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n6.a5

#### Authors

#### Abstract

In this paper, we prove semiclassical resolvent estimates for operators with normally hyperbolic trapping which are lossless relative to non-trapping estimates but take place in weaker function spaces. In particular, we obtain non-trapping estimates in standard $L^2$ spaces for the resolvent sandwiched between operators which localize away from the trapped set $\Gamma$ in a rather weak sense, namely whose principal symbols vanish on $\Gamma$.