Domination Problems In Weighted Bergman Spaces

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,?>-1,Ta(z)=(z+a)/(1+(?)z) for a?D.If|b|>(?),then Ta(?)bz in A?2(D).2.Let b?D.If|b|?(?)/(?2 + 14? + 60),then(z-b)2(?)z(1-bz)2 in A?2(D).3.Suppose that ?>-1,and denote Ta(z)=(z+a)/(1+(?)z) for a ?D.(?)Let p ?(0,1).If|a|?(B(p+1,?+1)-B(2,?+1))/(B(1,?+1)-B(p + 2,?+1)),then Ta(?)|z|p in L?2(D).(ii)Let p ?[1,+?).If|a|?(B(2,?+1)-B(p + 1,?+1))/(B(1,?+1)-B(p+2,?+1)),then |z|p(?)Ta in L?2(D).Additionally,we also discuss the concave and convex problems.