Geodesic
Homotopy formulas for the $\overline\partial$-operator on $\mathbf CP^n$ and the Radon--Penrose transform
Izvestiya. Mathematics , Tome 28 (1987) no. 3, pp. 555-587

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Global integral representations are constructed for differential forms on domains in complex projective space $\mathbf CP^n$. Consequences of these representations are the following: first, criteria for the solvability of the inhomogeneous Cauchy–Riemann equations on $q$-pseudoconvex and $q$-pseudoconcave domains in an algebraic manifold; second, explicit formulas and bounds for solutions of these equations; and third, a description of the kernel and image and an inversion formula for the Radon-Penrose transform of $(0,q)$-forms on $q$-linearly concave domains in $\mathbf CP^n$. Bibliography: 23 titles. 
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     author = {P. L. Polyakov and G. M. Henkin},
     title = {Homotopy formulas for the $\overline\partial$-operator on $\mathbf CP^n$ and the {Radon--Penrose} transform},
     journal = {Izvestiya. Mathematics },
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P. L. Polyakov; G. M. Henkin. Homotopy formulas for the $\overline\partial$-operator on $\mathbf CP^n$ and the Radon--Penrose transform. Izvestiya. Mathematics , Tome 28 (1987) no. 3, pp. 555-587. http://geodesic.mathdoc.fr/item/IM2_1987_28_3_a5/