Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties (Translations of Mathematical Monographs) by L. A. Aizenberg and Sh. A. Dautov (PDF)

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The authors consider the problem of characterizing the exterior differential forms which are orthogonal to holomorphic functions (or forms) in a domain $Dsubset {mathbf C}^n$ with respect to integration over the boundary, and some related questions. They give a detailed account of the derivation of the Bochner-Martinelli-Koppelman integral representation of exterior differential forms, which was obtained in 1967 and has already found many important applications. They study the properties of $overline partial$-closed forms of type $(p, n – 1), 0leq pleq n – 1$, which turn out to be the duals (with respect to the orthogonality mentioned above) to holomorphic functions (or forms) in several complex variables, and resemble holomorphic functions of one complex variable in their properties.

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