Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (5): 1971-1980.doi: 10.1007/s10473-022-0514-0

• Articles • Previous Articles    

GLEASON’S PROBLEM ON THE SPACE Fp,q,s (B) IN Cn

Pengcheng TANG, Xuejun ZHANG   

  1. College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China
  • Received:2020-11-13 Revised:2022-05-30 Published:2022-11-02
  • Contact: Xuejun Zhang,E-mail:xuejunttt@263.net E-mail:xuejunttt@263.net
  • Supported by:
    The research was supported by the National Natural Science Foundation of China (11942109) and the Natural Science Foundation of Hunan Province (2022JJ30369).

Abstract: Let Ω be a domain in Cn and let Y be a function space on Ω. If aΩ and gY with g(a)=0, do there exist functions f1,f2,,fnY such that g(z)=nl=1(zlal) fl(z)   for all z=(z1,z2,,zn)Ω ?

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.

Key words: boundary general function space, Gleason’s problem, solvability, unit ball

CLC Number: 

  • 32A37
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