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

Abstract

AbstractLet Ω ⊂ Rn be a bounded convex domain with C 2 boundary. Given 0 < p, q ≤ ∞ and a normal weight function φ (r ), let Hp,q,φ be the harmonic mixed norm space on Ω. In this paper we prove that Gleason's problem (Ω, a , Hp,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 Cn are obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)