A remark on unique continuation for the Cauchy-Riemann operator

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