The authors present a construction for an integral transform from sections of a vector bundle over a given manifold into Dolbeault cohomology of a related holomorphic vector bundle over another manifold. If \(Y @> \rho>> X\), \(Y @>\pi>> Z\) is a double fibration of smooth manifolds with \(Z\) having a complex structure, then the integral transform \({\mathcal S}\): \(\Gamma(X, V) \to H^S(Z, {\mathcal O}(E))\) is obtained for a suitable vector bundle \(V\) on \(X\) and a holomorphic vector bundle \(E\) on \(Z\). In the case of appropriate homogeneous situations the transform \(\mathcal S\) coincides with a certain representation theoretic intertwining operator.