The Composition Operator And Composition Operator Sequences On Several Analytic Function Spaces

B_n is the unit ball of(?)ⁿ (simplified by B) , (?): B → B is a holomorphic function taking B into itself, F is a space of holomorphic functions defined on B . f ∈ F,the composition operator C(?) is the operator on F given by C(?)(f) = f(?) . This paper investigates the collective compactness of composition operator sequences between different Weighted Dirichlet spaces defined on the unit ball of(?)2 in terms of measure.In addition,we character the boundedness and compactness of the composition operator on B_log(B).Define the Weighted Bloch SpaceB_log(Uⁿ)to be the set of all holomorphic functions f on Uⁿ for whichwhere Uⁿ = {z = (z₁,… ,z_n) : |z_i| < 1,i = 1, … ,n} is the unit polydisc of (?)n,we discuss the boundedness and compactness of the composition operator on B_log(Uⁿ) , and obtain some necessary and sufficient conditions.