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.
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