We solve the following Dirichlet problem on the bounded balanced domain $\Omega$ with some additional properties: For $p>0$ and a positive lower semi-continuous function $u$ on $\partial \Omega$ with $u\left(z\right)=u\left(\lambda z\right)$ for $\left|\lambda \right|=1$, $z\in \partial \Omega$ we construct a holomorphic function $f\in 𝕆\left(\Omega \right)$ such that $u\left(z\right)={\int }_{𝔻z}{\left|f\right|}^{p}d{𝔏}_{𝔻z}^2$ for $z\in \partial \Omega$, where $𝔻=\{\lambda \in ℂ|\lambda |<1\}$.