The boundary behavior of components of polyharmonic functions

We consider the following representation of polyharmonic functions on the unit ball $D^m$:
$$ f=\Phi_0+(1-r^2)\Phi_1+\dots+(1-r^2)^{n-1}\Phi_{n-1}, $$
where the $\Phi_j$ are harmonic on $D^m$ . We study the relation between uniform boundary properties of $f$ (its smoothness and growth while approaching the boundary) and the same properties of the terms in this representation. The theorems proved in this paper generalize some results obtained by Dolzhenko in the theory of polyanalytic functions.