Harmonic spirallike functions and harmonic strongly starlike functions

In this note, we define two subclasses of normalized harmonic univalent functions of the unit disk, spirallike functions and strongly starlike functions, which preserve a hereditary property and have nice analytic and geometric characterizations. We also investigate the uniform boundedness and quasiconformal extendability of strongly starlike functions. Some coefficient conditions can be given for strong starlikeness and spirallikeness. We consider a special form of harmonic functions as an application.