| Let C denote the complex plane,D denote the open unit disk,D = {z|z ∈C,|z|<1}.In this thesis,we mainly consider the domination in weighted Bergman spaces.And we obtain the following results:1.Suppose that b is a constant,α>-1,Ta(z)=(z+a)/(1+(?)z) for a∈D.If|b|>(?),then Ta(?)bz in Aα2(D).2.Let b∈D.If|b|≤(?)/(α2 + 14α + 60),then(z-b)2(?)z(1-bz)2 in Aα2(D).3.Suppose that α>-1,and denote Ta(z)=(z+a)/(1+(?)z) for a ∈D.(ⅰ)Let p ∈(0,1).If|a|≤(B(p+1,α+1)-B(2,α+1))/(B(1,α+1)-B(p + 2,α+1)),then Ta(?)|z|p in Lα2(D).(ii)Let p ∈[1,+∞).If|a|≤(B(2,α+1)-B(p + 1,α+1))/(B(1,α+1)-B(p+2,α+1)),then |z|p(?)Ta in Lα2(D).Additionally,we also discuss the concave and convex problems. |
