The Grushin operator on \({\mathbb R}^{d_1}\times{\mathbb R}^{d_2}\) is defined by \[ L=-\Delta_{x'}-|x'|^2\Delta_{x''}, \]
where \((x',x'')\in{\mathbb R}^{d_1}\times{\mathbb R}^{d_2}\) and \(\Delta_{x'}\) and \(\Delta_{x''}\) are the Laplacians in the variables \(x'\) and \(x''\).
The authors of the article under review find conditions on a function \(F\), under which the operator \(F(L)\) has weak type \((1,1)\) or is bounded on \(L^p\) with \(1<p<\infty\).