  It is well known that every Hoelder-continuous function on the unit circle is
the sum of two functions such that one of these two functions extends
holomorphically into the unit disc and the other extends holomorphically into
the complement of the unit disc. In the paper we prove that an analogue of this
holds for Hoelder-continuous functions on an annulus A which have zero averages
on all circles contained in A which surround the hole.
