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Gleason’s problem in weighted Bergman space on egg domains

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Abstract

It is shown that on the egg domains:

$$\Omega _a = \{ \xi = (z,w) \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}w \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}|z|^2 + |w|^{2/a}< 1\} ,{\bf{ }}0< a \leqslant 2$$

Gleason’s problem can be solved in the weight Bergman space. As an application, multiplier theorem on the egg domains is obtained.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China

    Guangbin Ren & Jihuai Shi

Authors
  1. Guangbin Ren
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  2. Jihuai Shi
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Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 19571077) and the State Education Commission Doctoral Foundation of China.

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Ren, G., Shi, J. Gleason’s problem in weighted Bergman space on egg domains. Sci. China Ser. A-Math. 41, 225–231 (1998). https://doi.org/10.1007/BF02879040

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  • DOI: https://doi.org/10.1007/BF02879040

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