[For the entire collection see Zbl 0742.00067.]The Penrose transform is always based on a diagram of homogeneous spaces. Here the case corresponding to the orthogonal group is studied by means of Clifford analysis [see F. Brackx, R. Delanghe and 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).
@article{701482,
title = {The Penrose transform and Clifford analysis},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1991},
pages = {[97]-104},
mrnumber = {MR1151894},
zbl = {0753.58033},
url = {http://dml.mathdoc.fr/item/701482}
}
Bureš, J.; Souček, V. The Penrose transform and Clifford analysis, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1991), pp. [97]-104. http://gdmltest.u-ga.fr/item/701482/