  In this paper we establish some new $L^{2}-L^{2}$ Carleman estimates for the
Baouendi-Grushin operators $\mathscr{B}_\gamma$, in (1.1) below. We apply such
estimates to obtain: (i) an extension of the Bourgain-Kenig quantitative unique
continuation; (ii) the strong unique continuation property for some degenerate
sublinear equations.
