On boundary properties of the components of polyharmonic functions (Q1280602)

A function \(f\in\mathbb{C}^n(G)\), \(G\subset\mathbb{C}\), is called \(n\)-analytic if \(\partial^nf/\partial\overline z^n=0\). Such a function can be represented (in a unique way) as \(f(z)=\varphi_0(z)+\overline z\varphi_1(z) +\cdots +\overline z^{n-1}\varphi_{n-1}(z)\), \(\varphi_k\) being holomorphic in \(G\). The main result of the paper is as follows: \(f\) is uniformly continuous of order \(p\) (or of boundedness of order \(p)\) in \(G\) if the same is true for all its holomorphic components \(\varphi_k\). Some related results are obtained, too.