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

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Abstract

Let Ω be a bounded convex domain with C 2 boundary in ℂn and for given 0 < p, q ⩽ ∞ and normal weight function ϕ(r) let H p,q,ϕ be the mixed norm space on Ω. In this paper we prove that the Gleason’s problem (Ω,a,H p,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 H p,q,ϕ .

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Authors and Affiliations

  1. Department of Mathematics, Huzhou Teachers College, 313000, Huzhou, China

    Zhangjian Hu

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  1. Zhangjian Hu
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Correspondence to Zhangjian Hu.

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Hu, Z. The Gleason’s problem on mixed norm spaces in convex domains. Sci. China Ser. A-Math. 46, 827–837 (2003). https://doi.org/10.1360/02ys0248

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