A Family of Lempert Domains

In Ghosh and Zwonek (2-proper holomorphic images of classical Cartan domains. https://doi.org/10.48550/arXiv.2303.11940 ) introduced a new class of domains Lₙ L n , n≥ 1 n ≥ 1 , which are 2-proper holomorphic images of the Cartan domains of type four. This family contains biholomorphic images of the symmetrized bidisc and the tetrablock. It is well-known, that symmetrized bidisc and tetrablock are Lempert domains. In our paper we show that the whole family of domains Lₙ L n are Lempert domains.