Omitted rays and wedges of fractional Cauchy transforms

R. A. Hibschweiler, T. H. Macgregor
2006 Journal of the Australian Mathematical Society  
For or > 0 let & a denote the set of functions which can be expressed where /x is a complex-valued Borel measure on the unit circle. We show that if / is an analytic function in A = (z € C : \z\ < 1) and there are two nonparallel rays in C\/(A) which do not meet, then / e & a where an denotes the largest of the two angles determined by the rays. Also if the range of a function analytic in A is contained in an angular wedge of opening an and 1 < a < 2, then / e & a .
doi:10.1017/s1446788700014075 fatcat:id25hv62lzfnvejiourn4kumzu