Hilbert spaces of holomorphic functions on generalized Cartan–Hartogs domains

Abstract

In this article, we introduce invariant Hilbert spaces of holomorphic functions on generalized Cartan–Hartogs domains, whose reproducing kernels can be explicitly expressed, and provide integral formulae for the invariant inner products.

Keywords:

• Cartan domain
• generalized Cartan–Hartogs domain
• dual generalized Cartan–Hartogs domain
• reproducing kernel

AMS Subject Classification:

• 32A25

Acknowledgements

This research was supported by the Scientific Research Fund of SiChuan Provincial Education Department (11ZA156). The author thanks anonymous referees for their valuable comments which led to the improvement of this article.