Abstract
We obtain new generalized Hua’s inequality corresponding to YIV(N,n;K), where YIV(N,n;K) denotes the fourth Cartan-Hartogs domain in CN+n. Furthermore, we introduce the weighted Bloch spaces on YIV(N,n;K) and apply our inequality to study the boundedness and compactness of composition operator Cϕ from βp(YIV(N,n;K)) to βq(YIV(N,n;K)) for p≥0 and q≥0.
Highlights
The study of composition operators on various Banach spaces of analytic functions has been a long active field in complex and functional analysis
The composition operators as well as related operators known as the weighted composition operators between the Bloch space and Lipschitz space were investigated in [1, 2] in the case of the unit disk
In 2000, Yin constructed four kinds of domains corresponding to the classical bounded symmetric domains, called the Cartan-Hartogs domains [10]
Summary
The study of composition operators on various Banach spaces of analytic functions has been a long active field in complex and functional analysis. The study of the composition operators on the Bloch space was given in [3] for the polydisc, in [4, 5] for the unit ball, and in [6,7,8,9] for the bounded symmetric domains. It is known that the Cartan-Hartogs domains are nonhomogeneous domains except the unit ball It is different from the bounded symmetric domains. In 2015, Su et al obtained generalized Hua’s inequality corresponding to the first Cartan-Hartogs domain YI (see Theorem 1 in [13]). We will obtain some results about the composition operators for the case of the weighted Bloch space on the fourth Cartan-Hartogs domain. We give the sufficient conditions and necessary conditions for the boundedness (in Section 3) and the compactness (in Section 4) of composition operator Cφ from βp(YIV) to βq(YIV), where p ≥ 0, q ≥ 0
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