Local smoothing for the Hermite wave equation
Local smoothing for the Hermite wave equation
We show local smoothing estimates in $L^p$-spaces for solutions to the Hermite wave equation. For this purpose, we obtain a parametrix given by a Fourier Integral Operator, which we linearize. This leads us to analyze local smoothing estimates for solutions to Klein-Gordon equations. We show $\ell^2$-decoupling estimates adapted to the …