Abstract
In this paper, we discuss the relationship between the adjoints of linear fractional composition operators with respect to two equivalent norms on the Dirichlet space of the disk or the ball. We give a simple and insightful connection between these two norms using the backward shift and the Volterra integration operator. More explicit formulas for the adjoints of linear factional composition operators on the Dirichlet space of the disk or the ball are obtained.
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