HILBERT-VALUED FORMS AND BARRIERS ON WEAKLY PSEUDOCONVEX DOMAINS

We introduce an alternative proof of the existence of certain Ck barrier maps, with polynomial explosion of the derivatives, on weakly pseudoconvex domains in Cn. Barriers of this sort have been constructed very recently by J. Michel and M.-C. Shaw, and have various applications. In our paper, the adaptation of Hõrmander’s L2 techniques to suitable vector-valued functions al-lows us to give a very simple approach of the problem and to improve some aspects of the result of Michel and Shaw, regarding the explosion of the barrier and the regularity assumption on the domain. Introduction and statement of results Let › be a bounded weakly pseudoconvex domain in Cn with Lip1 boundary @ › and let › ⁄ be a bounded domain with Lip1 boundary such that „ › ‰ ›⁄. Put U = ›⁄n„›. The aim of the present paper is to give