关于某些调和函数

用H表示形如f(z)=h(z) g(z)的调和函数族,其中h和g是单位圆盘内的解析函数.本文考虑H的三类子族函数.其中的两族为PH(α)=f∶Ref(z)z≥α和NH(α)=f∶Ref(z)θz≥θα,其中0≤α<1和θ=argz.本文得到了函数f属于其中一族的一个充分必要条件,并且获得了一些系数不等式和偏差定理.

On Certain Classes of Harmonic Functions

Let H be the class of harmonic function of the form f(z)=h(z)+—g(z),where h and g are analytic in the unit disk Δ={z∶|z|＜1}. We consider three subclasses of H. Two of them are PH(α)={f∶Re(f(z)/z)(>-)α} and NH(α)={f∶Re((e)f(z))/((e)θ)((e)z)/((e)θ)(>-)α}, where 0(>-)α＜1 and θ=arg z. A sufficient and necessary condition that the function f belongs to one of these classes is shown. Some coefficient inequalities and distortion properties are obtained.