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

Document Type : Original Article

Authors

1 Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran

2 Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran

Abstract

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.

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