Abstract
For
$n\geq 3$
, let
$Q_n\subset \mathbb {C}$
be an arbitrary regular n-sided polygon. We prove that the Cauchy transform
$F_{Q_n}$
of the normalised two-dimensional Lebesgue measure on
$Q_n$
is univalent and starlike but not convex in
$\widehat {\mathbb {C}}\setminus Q_n$
.
A mixed norm estimate for the X-ray transform