The Penrose transform and Clifford analysis

summary:[For the entire collection see Zbl 0742.00067.]\par The Penrose transform is always based on a diagram of homogeneous spaces. Here the case corresponding to the orthogonal group $SO(2n,C)$ is studied by means of Clifford analysis [see {\it F. Brackx, R. Delanghe} and {\it F. Sommen}: Clifford analysis (1982; Zbl 0529.30001)], and is presented a simple approach using the Dolbeault realization of the corresponding cohomology groups and a simple calculus with differential forms (the Cauchy integral formula for solutions of the Laplace equation and the Leray residue for closed differential forms)