The Gleason?s problem on mixed norm spaces in convex domains

Abstract

Let Ω be a bounded convex domain with C2 boundary in ℂn and for given 0 < p, q ⩽ ∞ and normal weight function ϕ(r) let Hp,q,ϕ be the mixed norm space on Ω. In this paper we prove that the Gleason’s problem (Ω,a,Hp,q,ϕ is solvable for any fixed point a ∈ Ω. While solving the Gleason’s problem we obtain the boundedness of certain integral operator on Hp,q,ϕ.