Weak Factorization For Weighted Bergman Spaces Over The Siegel Upper Half-space

In this thesis,we estblish weak factorizations for a weighted Bergman space A_α^p（U）,with 1<p<∞,into two weighted Bergman spaces over the Siegel upper half-space of Cⁿ.We first use the atomic decomposition theorem and duality in A_α^p（U）to characterize the equivalent conditions of boundedness of Hankel forms and small Hankel operator,by the equivalence between weak factorization and the boundedness of Hankel forms,the weak factorization for A_α^p（U）as follows A_β^q（U）=A_α1^p1（U）（?）A_α2^p2（U）,where q>0,α>-1,p₁,p₂>0 andα₁,α₂>-1,satisfying1/p₁+1/p₂=1/q,α₁/p₁+α₂/p₂=β/q.