HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS

Abstract

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