A sharp multiplier theorem for Grushin operators in arbitrary dimensions (Q2256073)

The authors obtain a sharp \(L^p\) spectral multiplier theorem for the Grushin operator \[ L=-\sum_{j=1}^{d_1}\partial_{x_j}^2-\left(\sum_{j=1}^{d_1}|x_j|^2\right)\sum_{j=1}^{d_2}\partial_{y_j}^2 \] on \(\mathbb{R}^{d_1}\times\mathbb{R}^{d_2}\) with \(d_1<d_2.\) The case \(d_1\geq d_2\) was considered by the first author and \textit{A. Sikora} [Math. Res. Lett. 19, No. 5, 1075--1088 (2012; Zbl 1288.47044)].