Gleason's problem for harmonic mixed norm and Bloch spaces in convex domains

✍ Scribed by Zhangjian Hu

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 210 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310353

✦ Synopsis

Abstract

Let Ω ⊂ R^n^ be a bounded convex domain with C ^2^ boundary. Given 0 < p, q ≤ ∞ and a normal weight function φ (r ), let H~p,q,φ~ be the harmonic mixed norm space on Ω. In this paper we prove that Gleason's problem (Ω, a , H~p,q,φ~ ) is always solvable for any reference point a ∈ Ω. Also, Gleason's problem for the harmonic φ ‐Bloch (little φ ‐Bloch) space is solvable. The parallel results for the holomorphic functions on bounded convex domains in C^n^ are obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)