Subellipticity of the $\bar{\mathrm{\partial }}$-Neumann problem on a weakly $q$-pseudoconvex/concave domain

For a domain $D$ of ${\mathbb{C}}^n$ which is weakly $q$-pseudoconvex or $q$-pseudoconcave we give a sufficient condition for subelliptic estimates for the $\bar{\mathrm{\partial }}$-Neumann problem. The paper extends to domains which are not necessarily pseudoconvex, the results and the techniques of Catlin. MSC: 32D10, 32U05, 32V25