Journal of the
Korean Mathematical Society JKMS

Let $\{ \Omega_\tau\}_{\tau \in I}$ be a family of strictly convex domains in ${\mathbb C}^n$. We obtain explicit estimates for the solution of the $\bar{\partial}$-equation on $\Omega \times I$ in H\"older space. We also obtain explicit point-wise derivative estimates for the $\bar{\partial}$-equation both in space and parameter variables.

Keywords: H\"older estimates, integral representation for $\bar{\partial}$, Cauchy-Riemann equation

MSC numbers: 32W05, 32W10