A boundary analogue of Morera’s theorem in the unit ball of 𝐶ⁿ

Grinberg, Eric L.

doi:10.1090/S0002-9939-1988-0915726-5

A boundary analogue of Morera’s theorem in the unit ball of $\textbf {C}^n$
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Proc. Amer. Math. Soc. 102 (1988), 114-116 Request permission

Abstract:

We show that the boundary values of holomorphic functions in the unit ball of ${{\mathbf {C}}^n}(n{\text { > 1)}}$ are characterized by the vanishing of their contour integrals over certain closed curves.

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