Generalization of Morrey–Kohn–Hörmander’s Formula

We extend the Morrey–Kohn–Hörmander formula to a larger set of sections in \({\mathcal {C}}^{(p, q)}(\overline{\Omega }, E)\) ${\mathcal{C}}^{(p,q)}(\overline{\mathrm{\Omega }},E)$ beyond \({{\,\textrm{Dom}\,}}(\bar{\partial }^*)\) $\text{Dom}({\overline{\partial }}^{\ast })$ . This extension is useful for making estimates for a section not in \({{\,\textrm{Dom}\,}}(\bar{\partial }^*)\) $\text{Dom}({\overline{\partial }}^{\ast })$ .