A Littlewood-type Theorem For Weighted Bergman Functions

In this paper,we study the Littlewood-type theorem for weighted Bergman func-tions.Let{X_n}_n?0be standard Bernoulli or Steinhaus or Gaussian random variable sequences,f(z)=??^?_n=0a_nzⁿ,(Rf)(z)=??^?_n=0a_nX_n(?)zⁿbe the randomization of f.We begin with three examples,and obtain the sufficient and necessiary conditions of Rf^a.?^s.L_a^q(d A?)for each f?L_a^p(d A?).During the study,we find that coefficient multi-pliers is an important tool,so we summarize the conclusion of coefficient multipliers.