Lp estimates for the wave equation associated to the Grushin operator

preprint2012arXivOpen access

Abstract

We prove that the solution of the wave equation as- sociated to the Grushin operator G=−Δ+∣x∣2∂t2 G = -Δ+|x|^2 \partial_t^2 is bounded on Lp(Rn+1)(1<p<∞) L^p(R^{n+1})(1 < p < \infty), when ∣1/p−1/2∣<1/n+2|1/p- 1/2 | < 1/n+2 .

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