In this talk, I shall talk about analogues of pseudo-differential
operators (pseudo-multipliers) associated with the joint functional
calculus for the Grushin operator. In particular, we shall discuss
some sufficient conditions on a symbol function which imply
$L^2$-boundedness of the associated Grushin pseudo-multiplier. This
talk is based on a joint work (arXiv:2111.10098) with Sayan Bagchi.