Diederich-Fornæss index and global regularity of the complex Green operator: domains with comparable Levi eigenvalues

Let $\mathrm{\Omega }\subset {\mathbb{C}}^n$, with $n\ge 3$, be a smooth bounded pseudoconvex domain satisfying the symmetric eigenvalue comparability condition $D(q_0)$ for some $1\le q_0\le n-2$. We show that if the Diederich-Fornaess-index of $\mathrm{\Omega }$ is one, then the complex Green operator $G_q$, associated with $\mathrm{\Omega }$, is globally regular for $q$ in the range $\min \{q_0,n-1-q_0\}\le q\le \max \{q_0,n-1-q_0\}$.