关于某些调和函数(英文)

On Certain Classes of Harmonic Functions

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.

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 △= {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（δf（z）/δθ/δz/δθ ≥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.