# HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS

• Published : 2011.03.01

#### Abstract

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$\ddot{o}$lder space. We also obtain explicit point-wise derivative estimates for the $\bar{\partial}$-equation both in space and parameter variables.

#### Acknowledgement

Supported by : KRF, Sogang University

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