Residue integral formulas and the Radon transform for differential forms onq-linearly concave domains

Abstract

Let D be the q-linearly concave domain in the n-dimensional complex projective space CP n, i.e. for any point z ~ D there exists q-dimensional complex projective subspace A(z) c D containing the point z and smoothly depending on z ~ D. The concept of a q-linearly concave domain [8, 15] is useful specialization of fundamental notion of q-concave manifold [1]. In development of Andreotti-Grauert theory of cohomology of q-concave manifolds [1, 11,13] it was constructed [3, 15] global integral homotopy formulas for the 8-operator in q-concave domains. Based on [15] we prove here a new global integral representation formulas