Abstract
The problem of characterizing the restrictions of pluriharmonic functions to real hypersurfaces of a complex manifold has been studied by several authors (cf. [AN], [Au], [B], [BF], [Fi], [M], [R], [S], [TdB]). In this paper we take up the analogous question for abstract CR manifolds of arbitrary CR codimension. We think that this investigation will be relevant to improve and extend to the abstract case some of the results on global CR cohomology recently obtained in [HN]. After fLxing notations and definitions in w 1, we introduce in w 2 the notions of CR gauges and trasversal 1-jets. Pluriharmonic functions are then defmed in w 3, where decomposition and extension theorems are also proved. In w 4 we finally discuss cohomology groups with coefficients in the sheaf of pturiharmonic functions and cohomology groups associated to related differential complexes.
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