We establish the L 2 theory for the Cauchy–Riemann equations on product domains
provided that the Cauchy–Riemann operator has closed range on each factor. We deduce …

An $ L^ 2$ version of the Serre duality on domains in complex manifolds involving duality of
Hilbert space realizations of the $\overline {\partial} $-operator is established. This duality is …

The Hartogs triangle serves as an important example in several complex variables. The
Hartogs triangle is pseudoconvex, but its boundary is not Lipschitz, yet rectifiable. In this …

Let X be a complex manifold. The study of the closed-range property of the Cauchy–
Riemann equations is of fundamental importance both from the sheaf theoretic point of view …

The purpose of this article is to establish sufficient conditions for the closed range of∂(and∂
b) on not necessarily pseudoconvex domains (and their boundaries) in Stein manifolds. We …

In this paper, we study a sufficient condition for subelliptic estimates in the weak Z (k)
domain with C3 boundary in an n-dimentionsl Steinmanifold X. Consequently, the …

The global boundary regularity for the∂-problem on a relatively compact domain with the
C2-smooth boundary in a Kähler manifold that satisfies some “Hartogs-pseudoconvexity” …

In this paper it is shown that the Hartogs triangle T in C 2 is a uniform domain. This implies
that the Hartogs triangle is a Sobolev extension domain. Furthermore, the weak and strong …

For certain annuli in ℂ ⁿ, n≥ 2, with non-smooth holes, we show that the∂ ̄-operator from L
² functions to L ² (0, 1)-forms has closed range. The holes admitted include products of …

Abstract Let Ω= Ω ∖ D Ω= Ω~\D¯ where Ω Ω~ is a bounded domain with connected
complement in C^ n C n (or more generally in a Stein manifold) and D is relatively compact …