The Grushin operator is defined as $G:=-\triangle-|x|^2\partial_t^2$ on R^{n+1}. We study the boundedness of the multipliers $m(G)$ of $G$ 
 on $L^p(R^{n+1})$. We prove the analogue of the Hormander-Mihlin theorem for $m(G)$. We  also study the boundedness of the solution of the 
 wave equation corresponding to $G$ on $L^p(R^{n+1})$. The main tool in studying the above is the operator-valued Fourier multiplier theorem 
 by Lutz Weis. Next we look at Toeplitz operators on some Segal-Bargmann spaces. Let $T_g$ be the Toeplitz operator corresponding to g. We 
 study the boundedness of $T_g$ by transferring them to the underlying $L^2$ spaces. We make use of the above transference to get some 
 sufficient conditions on $g$ for the boundedness of $T_g$.