2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152172We give a generalization of the Penrose transform on Hermitian manifolds with metrics locally conformally equivalent to Bochner-Kähler metrics. We also give an explicit formula for the inverse transform. This paper is a generalization of "The Twistor correspondence of the Dolbeault complex over $\C^n$" (dg-ga/9501004) and intended to supersede it.AMS-LaTeX v1.2, 30 pagesDifferential GeometryAlgebraic Geometry32L25 (Primary), 53C55, 32C35 (Secondary)text