By a theorem of Andreotti and Grauert if ω is a (p, q) current, q < n, in a Stein manifold, ∂̄ closed and with compact support, then there is a solution u to ∂̄u = ω still with compact support. The main result of this work is to show that if moreover ω ∈ L(dm), where m is a suitable Lebesgue measure on the Stein manifold, then we have a solution u with compact support and in L(dm). We prove it by...

We propose a new general version of Stein’s method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution which is based on a linear difference or differential-type operator. The resulting Stein identity highlights the unifying theme behind the literature on Stein’s method (both for continuous and discrete distributions)...