Möbius function of coordinate hyperplanes in complex ellipsoids

For $p_1,\dots,p_n>0$, let $\mathbb{E}=\{z\in\mathbb{C}^n:\sum_{j=1}^n\vert z_j\vert^{2p_j}<1\}$ be a complex ellipsoid. We present effective formulas for the generalized Möbius and Green functions $m_{\mathbb{E}}(A,\cdot)$, $g_{\mathbb{E}}(A,\cdot)$ in the case where $A:=\{z\in\mathbb{E}:z_1\cdots z_k=0\}$ ( $1\leq k\leq n$).