Extremal Problems on Super-Cartan Domain of the First Type

New classes of domains with explicit Bergman kernel

“…For Ω belonging to one of the four classical series, an explicit form of the Bergman kernel for Y (q, Ω; k) has been obtained by Weiping Yin ( [29], [30]).…”

“…Weiping Yin has got the Bergman kernel function in explicit form for these four Cartan-Hartogs domains [29], [30]. We would like to point out that if we can get the Bergman kernel in explicit form for a domain, then this domain is a good domain for research.…”

Boundedness and Compactness of Weighted Composition Operators from α-Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind

“…In 1998, building on the notion of bounded symmetric domains, Yin and Roos constructed a new type of domain called the Cartan-Hartogs domain [3], and Yin introduced the so-called Hua domains [4], which include the Cartan-Hartogs domains, the Cartan-Egg domains, the Hua domains, the generalized Hua domains, and the Hua construction. The generalized Hua domains are defined as follows:…”

Boundedness and Compactness of Weighted Composition Operators from α-Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind

“…where Z denotes the transpose of Z, Z denotes the conjugate of Z, and m, n, p, q are positive integers. In 1998, building on the notion of bounded symmetric domains, Yin and Roos constructed a new type of domain called the Cartan-Hartogs domain [3], and Yin introduced the so-called Hua domains [4], which include the Cartan-Hartogs domains, the Cartan-Egg domains, the Hua domains, the generalized Hua domains, and the Hua construction. The generalized Hua domains are defined as follows:…”