在微分算子作用下调和函数的单叶半径估计

基于单叶调和函数系数模估计的猜想, 在调和函数f(z)=h(z)+g(z)^-的系数模满足猜想条件下,研究 f(z)在L=z?/(?z)-(-overz)?/(?(-overz))作用下的单叶半径问题,分别得到精确的单叶半径表达式.结果表明:在系数模估计满足更一般表达式的条件下,同样也能得到在L作用下L(f)的精确单叶半径估计.

On the Estimates of Univalent Radius for Harmonic Mappings under the Differential Operator

Let f(z)=h(z)+g(z)^- be a harmonic mapping on the unit disk D={z||z|<1}, L represents the differential operator L=z?/(?z)-(-overz)?/(?(-overz)). Under the coefficients satisfying two famous conjecture bounds for univalent harmonic functions on D, we obtain two sharp univalent radii for L_f(z)=z(?f)/(?z)-(-overz)(?(-overf))/(?(-overz)). Moreover, with the condition that the coefficients satisfying one general expression, we also obtain the similar sharp result.