J. Aust. Math. Soc.
80 (2006), 367373

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



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 complexvalued 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
.

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