Linear Fractional Composition Operators On The Harmonic Dirichlet Space In The Unit Ball

In this paper we study the adjoint of linear fractional composition operators on the harmonic Dirichlet space in the unit ball, and discuss their normality and essentially normality on Dh(BN) and Dh0(BN).In the first chapter, we introduce some related background and some well-known results on composition operators.In the second chapter, we introduce some basic definitions and properties of the harmonic Dirichlet space in the unit ball and linear fractional composition operators.In the third chapter, we discuss the adjoint of linear fractional composition opera-tors on the harmonic Dirichlet space in the unit ball.Then we put forward the sufficient and necessary condition for a linear fractional composition operator to be unitary.In the fourth chapter, we study normality and essentially normality of linear frac-tional composition operators on Dh(BN) and Dho(BN).