HOMOTOPY FORMULAS FOR THE $ \bar\partial$-OPERATOR ON<b>C</b><i>Pⁿ</i>AND THE RADON-PENROSE TRANSFORM

Abstract

Global integral representations are constructed for differential forms on domains in complex projective space CPn. 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 CPn. Bibliography: 23 titles.