A remark on unique continuation for the Cauchy-Riemann operator

Abstract

In this note we obtain a unique continuation result for the differential inequality $|\bar{\partial }u|\le |Vu|$, where $\bar{\partial }=(i{\partial }_y+{\partial }_x)/2$ denotes the Cauchy-Riemann operator and $V(x,y)$ is a function in $L^2({\mathbb{R}}^2)$.

To appear in Bull. Korean Math. Soc., 5 pages