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Let be a domain with smooth boundary and . A holomorphic function on is called a () peak function at if , , and for all . If is strongly pseudoconvex, then peak functions exist. On the other hand, J. E. Fornaess constructed an example in to show that this result fails, even for functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function on a...
The Penrose transform gives an isomorphism between the kernel of the -Dirac operator over an affine subset and the third sheaf cohomology group on the twistor space. In the paper we give an integral formula which realizes the isomorphism and decompose the kernel as a module of the Levi factor of the parabolic subgroup. This gives a new insight into the structure of the kernel of the operator.
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