Linear combination of derivative weighted composition operators

Abstract

The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly, and for a combination of several derivative weighted composition operators which acts on classic Bergman space, the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators. Some similar results about composition operators on the Dirichlet space are also presented. A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.

Keywords

derivative weighted composition operator / Bergman space / Dirichlet space / essential norm

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