summary:Let φ be an entire self-map of CN, u0 be an entire function on CN and u=(u1,⋯,uN) be a vector-valued entire function on CN. We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator Tu0,u,φ as follows: \openup -.4pt T_{u_0,{\bf u},\varphi }f=u_0\cdot f\circ \varphi +\sum _{i=1}^Nu_i\cdot \frac {\partial f}{\partial z_i}\circ \varphi . We investigate the boundedness and compactness of Tu0,u,φ on Fock spaces. The complex symmetry and self-adjointness of Tu0,u,φ are also characterized
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