J. Aust. Math. Soc.  80 (2006), 367-373
Omitted rays and wedges of fractional Cauchy transforms

 R. A. Hibschweiler   University of New Hampshire   Department of Mathematics and Statistics   Durham, NH 03824   USA  rah2@cisunix.unh.edu
 and
 T. H. Macgregor   Bowdoin College   Department of Mathematics   Brunswick, ME 04011   USA

Abstract
For let denote the set of functions which can be expressed
where is a complex-valued Borel measure on the unit circle. We show that if is an analytic function in and there are two nonparallel rays in which do not meet, then where denotes the largest of the two angles determined by the rays. Also if the range of a function analytic in is contained in an angular wedge of opening and , then .