Abstract. Let Ω 1 , Ω 2 be two disjoint open sets in C n whose boundaries share a smooth real hypersurface M as relatively open subsets. Assume that Ω i is equipped with a complex structure J i which is smooth up to M . Assume that the operator norm J 2 − J 1 < 2 on M . Let f be a continuous function on the union of Ω 1 , Ω 2 , M . If f is holomorphic with respect to both structures in the open sets, then f must be smooth on the union of Ω 1 with M . Although the result as stated is far more meaningful for in…
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