Morera conditions along real planes and a characterization of CR functions on boundaries of domains in \(\mathbb{C}^ N\)
The paper deals with the problem whether a property of being a CR function on boundary \(bD\) of a bounded domain \(D \subset \mathbb{C}^ N\) can be described by Morera conditions on integrals against the forms with constant coefficients over intersections of the boundary \(bD\) with real affine planes (specially with real affine hyperplanes) in \(\mathbb{C}^ N\) that meet \(bD\) transversely. Theorems represent a generalization of some earlier results concerning criteria for CR functions with respect to complex affine planes in \(\mathbb{C}^ N\) that meet \(bD\) transversely in the paper by [\textit{J. Globevnik} and \textit{E. L. Stout}, Duke Math. J. 64, 571-615 (1991; Zbl 0760.32002)].
scientific article; zbMATH DE number 704913