Quasiconformal Extension of Strongly Spirallike Functions

We show that a strongly lambda-spirallike function of order alpha can be extended to a sin(pi alpha/2)-quasiconformal automorphism of the complex plane for -pi/2 < lambda < pi/2 and 0 < alpha < 1 with vertical bar lambda vertical bar < pi alpha/2. Towards the proof we provide several geometric characterizations of a strongly lambda-spirallike domain of order alpha. We also give a concrete form of the mapping function of the standard strongly lambda-spirallike domain U-lambda,U-alpha of order alpha. A key tool of the present study is the notion of lambda-argument, which was developed by Y. C. Kim and the author [5].