On holomorphic extension of functions on singular real hypersurfaces in ℂn

Abstract

The holomorphic extension of functions defined on a class of real hypersurfaces in ℂn with singularities is investigated. When n=2, we prove the following: every C1 function on Σ that satisfies the tangential Cauchy-Riemann equation on boundary of {(z,w)∈ℂ2:|z|k<P(w)}, P∈C1, P≥0 and P≢0, extends holomorphically inside provided the zero set P(w)=0 has a limit point or P(w) vanishes to infinite order. Furthermore, if P is real analytic then the condition is also necessary.