Quasiconformal extension of strongly spirallike functions

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