An Extremum Problem For The Bergman Norm Of Multiplications Of Mbius Transformations

In this thesis,we study the relationship between the Bergman morm of a finite Blaschke product and its zeros and obtain the following results:1.Let α∈D,p≥2.Then ||φ||p is an increasing function of |a|；2.Let |α|=ro<1.Then3. Let |α1|,|α3|<1/√3. Then ||φα1φα2||2 attains its minimum when α1=α2=0.4. Suppose 0 ≤ r< 1,p ≥2 and α1,α2,...,αn ∈rD. Then ||φα1φα2…φan||p attains its maximum if and onlly if α1=α2 =…αn and |α1|=r.