The $\bar \partial$-Neumann solution to the inhomogeneous Cauchy-Riemann equation in the ball in $\textbf {C}^{n}$

Abstract:

Let $\vartheta$ denote the formal adjoint of the Cauchy-Riemann operator $\overline \partial$ on ${{\mathbf {C}}^n}$, and let $N$ denote the Kohn-Neumann operator on the unit ball in ${{\mathbf {C}}^n}$. The operator $\vartheta \; \circ \;N$ provides a natural fundamental solution for $\overline \partial f = g$ on the ball. It is our purpose to present the kernel $P$ for this operator $\vartheta \; \circ \;N$ explicitly—the coefficients are exhibited as rational functions.