A decomposition of functions with zero means on circles

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.