Generalized study of the operator $\hat{I}\pm {\partial }^k{\bar{\partial }}^k+{\hat{I}}^2{\bar{\partial }}^k+{\hat{I}}^3{\partial }^k+c$ in weighted Hilbert space $L^2(\mathbb{C},{\mathrm{e}}^{-|z{|}^2})$

Eramane Bodian, Winnie Ossete Ingoba, Souhaibou Sambou +2

By Hörmander's $L^2$-method, we study the operator $\hat{I}\pm {\partial }^k{\bar{\partial }}^k+{\hat{I}}^2{\bar{\partial }}^k+{\hat{I}}^3{\partial }^k+c$ for any order $k$ with $\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3\in \mathbb{R}$ such…