Multiplier Properties Of Random Dirichlet Function

LetD,D(D)be the Dirichlet space and the double disk Dirichlet space.Cochran et al.prove that for function f(z)(28)?a_n z~n in D andf_w(z)(28)?X _na _n z~n,if{X _n(w)}is independent and identically distributed and satisfy the conditions thatE(|X _n|~2)??and-X_n have the same distribution asX_n,then f_w(z)is a multiplier of D.In the third chapter of this paper,almost all the conditions satisfying the conditions E(X _n)=0and anyP(X _n)are rational numbers function?X _n a_n z~n are the multipliers in D.In the fourth chapter oft this paper,Consider the multiplier problem onD(D~2).We prove that the randomization of a functions inD(D~2)are multipliers onD(D~2)almost surely,by using the embedding theorem on Sobolev space.