Bergman and Dirichlet spaces in the unit ball and symmetric lifting operator

Let Bn be the open unit ball in C n and B 2 n = Bn×Bn. The symmetric lifting operator which lifts analytic functions from H(Bn) to H(B 2 n ) 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.