SOLUTION TO $\overline{\partial}$ PROBLEM WITH EXACT SUPPORT AND REGULARITY FOR THE $\overline{\partial}$-NEUMANN OPERATOR ON WEAKLY q-CONVEX DOMAINS

Abstract

Let Ω be a weakly q-convex domain in ℂn. We establish the L2 existence theorem for the [Formula: see text]-Neumann operator N when the boundary of Ω is C1. Using this result, we study the [Formula: see text] problem with exact support on such domains. Furthermore, there exists a number ℓ0 > 0 such that the operators N, [Formula: see text] and the Bergman projection are regular in the Sobolev space Wℓ(Ω) for ℓ < ℓ0 when the boundary of Ω is C∞.