Reproducing Kernels of Some Weighted Bergman Spaces

Abstract

Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.

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Acknowledgements

G-T. Deng: This work was partially supported by NSFC (Grant Nos. 11971042, 11971045 and 12071035) and by SRFDP (Grant 20100003110004). T. Qian: The work is supported by the Macau Science and Technology foundation No.FDCT079/2016/A2, FDCT0123/2018/A3, and the Multi-Year Research Grants of the University of Macau No. MYRG2018-00168-FST.

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Correspondence to Yun Huang.

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Deng, GT., Huang, Y. & Qian, T. Reproducing Kernels of Some Weighted Bergman Spaces. J Geom Anal (2021). https://doi.org/10.1007/s12220-021-00616-1

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Keywords

  • Reproducing kernel
  • Reproducing kernel Hilbert space
  • Weighted Bergman spaces