On the Nikol'skij classes of polyharmonic functions (Q2714724)

Let \(D^m\) be the unit ball in \({\mathbb R}^m\). Then a polyharmonic function \(f\), \(\Delta^n f = 0\), in \(D^m\) can be decomposed by NEWLINE\[NEWLINE f = \sum^{n-1}_{k = 0} ( 1 - |x|^2)^k \Phi_k (x) , NEWLINE\]NEWLINE where \(\Phi_k\) are harmonic functions. The aim of the paper is to study to which extent properties of \(f\), expressed in terms of function spaces, are transferred to \(\Phi k\).NEWLINENEWLINEFor the entire collection see [Zbl 0952.00006].