Lp estimates for the wave equation associated to the Grushin operator

Abstract

We prove that the solution of the wave equation as- sociated to the Grushin operator $G=-\Delta +|x{|}^2{\partial }_t^2$ is bounded on $L^p(R^{n+1})(1<p<\infty )$, when $|1/p-1/2|<1/n+2$ .

Cited by in corpus (2)

• From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere
• Regularity of solutions to elliptic equations with Grushin's operator