Document Type : Original Article
Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran
Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran
Let Bn be the open unit ball in Cn and Bn×Bn. The symmetric lifting operator which lifts analytic functions from H(Bn) to H(Bn2) is defined as follow
L(f)(z,w) = f(z)-f(w)/z-w.
In this paper we investigate the action of symmetric lifting operator on the Bergman space in the unit ball. Also, we state a characterization for Dirichlet space and consider symmetric lifting operator on the Dirichlet space in the unit ball.