$L^2$-estimates for the $d$-operator acting on super forms

In the setting of super forms developed in a previous article by the author, we introduce the notion of $\mathbb{R}$-Kähler metrics on $\mathbb{R}^{n}$. We consider existence theorems and $L^{2}-$estimates for the equation $dα=β$, where $α$ and $β$ are super forms, in the spirit of Hörmander's $L^{2}-$estimates for the $\bar{\partial}-$equation on a complex Kähler manifold.

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