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Gleason’s Problem on the Space Fp,q,s (B) in ℂn

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Abstract

Let Ω be a domain in ℂn and let Y be a function space on Ω. If a ∈ Ω and g ∈ Y with g (a) = 0, do there exist functions f1, f2, ⋯, fn ∈ Y such that

$$g\left(z \right) = \sum\limits_{l = 1}^n {\left({{z_l} - {a_l}} \right)\,\,{f_l}\left(z \right)\,\,\,\,{\rm{for}}\,{\rm{all}}\,\,z = \left({{z_1},{z_2}, \cdots ,{z_n}} \right) \in \Omega \,?} $$

This is Gleason’s problem. In this paper, we prove that Gleason’s problem is solvable on the boundary general function space Fp,q,s (B) in the unit ball B of ℂn.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China

    Pengcheng Tang  (唐鹏程) & Xuejun Zhang  (张学军)

Authors
  1. Pengcheng Tang  (唐鹏程)
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  2. Xuejun Zhang  (张学军)
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Corresponding author

Correspondence to Xuejun Zhang  (张学军).

Additional information

The research was supported by the National Natural Science Foundation of China (11942109) and the Natural Science Foundation of Hunan Province (2022JJ30369).

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Tang, P., Zhang, X. Gleason’s Problem on the Space Fp,q,s (B) in ℂn. Acta Math Sci 42, 1971–1980 (2022). https://doi.org/10.1007/s10473-022-0514-0

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  • DOI: https://doi.org/10.1007/s10473-022-0514-0

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