Generalization of Hua's inequalities and an application

Abstract

Abstract. We generalize a new Hua's inequality and apply it to proof the boundedness of composition operator C φ from p-Bloch space β p (Y I (N,m,n;K)) to q-Bloch space β q (Y I (N,m,n;K)) in this paper, where Y I (N,m,n;K) denotes the first Cartan-Hartogs domain, and p 0 , q 0 .Mathematics subject classification (2010): 15A45, 47B33.

Multiplication operators on weighted Bloch spaces of the first Cartan domains

“…By the way, as an easy application of Lemma 6, we see that, for each Z, S ∈ I , the matrix I -ZS T is reversible. We also have the following result (see [20]).…”

“…We need the following result (see [20]) to obtain the point evaluation estimate for the Bloch functions.…”

Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain

“…Recently, Su et al in [21] obtained the necessary condition and sufficient condition for the boundedness and compactness of the composition operators from u-Bloch space to v-Bloch space on the first Hua domain. Su et al in [22] gave the necessary condition and sufficient condition for the boundedness and compactness of the composition operators from p-Bloch space to q-Bloch space on the first Cartan-Hartogs domain. The author characterized the bounded and compact weighted composition operators on the weighted Bers-type spaces of the Hua domains in [23].…”

Composition Operators from p-Bloch Space to q-Bloch Space on the Fourth Cartan-Hartogs Domains

“…In 2015, Su et al obtained generalized Hua's inequality corresponding to the first Cartan-Hartogs domain I (see Theorem 1 in [13]). From Theorem 1 in [13], it is easy to get more precise inequality (see Lemma 4).…”

“…From Theorem 1 in [13], it is easy to get more precise inequality (see Lemma 4). Furthermore, we obtain new generalized Hua's inequality corresponding to IV (see Lemma 5).…”