A Removability Result for Holomorphic Functions of Several Complex Variables

Suppose that Ω is a domain of Cn, n > 1, E ⊂ Ω closed in W, the Hausdorff measure H2n-1(E)=0, and f is holomorphic in Ω/E. It is a classical result of Besicovitch that if n = 1 and f is bounded, then f has a unique holomorphic extension to Ω. Using an important result of Federer, Shiffman extended Besicovitch’s result to the general case of arbitrary number of several complex variables, that is, for n > 1. Now we give a related result, replacing the boundedness condition of f by certain integrability conditions of f and of ∂2f/∂z2j, j=1,2,…,n.

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