Global approximation of CR functions on Bloom-Graham model graphs in ℂⁿ

Abstract

We define a class of generic CR submanifolds of C n \mathbb {C}^n of real codimension d d , 1 ≤ d ≤ n 1\leq d\leq n , called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem for Bloom-Graham model graphs with a polynomial growth assumption on their graphing functions.