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Is this true that any holomorphic functions in a domain with smooth boundary, and which is smooth on the boundary is a CR function ?

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Yes.

A CR function is by definition annihilated by a (0,1) vector field tangent to the boundary. But any (0,1) tangent vector to the boundary is a limit of (0,1) tangent vectors in the interior (which annihilate the function in the interior.)

Note that in one variable there are no (0,1)-vectors tangent to the boundary so each smooth function on the boundary is CR.

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