A Dolbeault lemma for temperate currents (Q2077178)

The classical Dolbeault lemma solves the Cauchy-Riemann equations for smooth differential forms on Stein manifolds. The author of the present paper carries this result over to temperate distributions on bounded Stein subdomains of Stein manifolds. This is not an immediate consequence of the classical case! In fact, the author relies heavily on Hörmander's estimates for the Cauchy-Riemann complex, on a ``well-known but never proved'' extension result for distributions -- the author proves it -- , and on Dobeault's original method for proving the classical case. The results presented are important and useful; the author's clear exposition accounts for pleasant reading.