HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS

Title & Authors
HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS
Cho, Sang-Hyun;

Abstract
Let $\small{\{\Omega_{\tau}\}_{\tau{\in}I}}$ be a family of strictly convex domains in $\small{\mathbb{C}^n}$. We obtain explicit estimates for the solution of the $\small{\bar{\partial}}$-equation on $\small{\Omega{\times}I}$ in H$\small{\ddot{o}}$lder space. We also obtain explicit point-wise derivative estimates for the $\small{\bar{\partial}}$-equation both in space and parameter variables.
Keywords
H$\small{\ddot{o}}$lder estimates;integral representation for $\small{\bar{\partial}}$;Cauchy-Riemann equation;
Language
English
Cited by
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