Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space

In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space.     

Weighted Composition Operators From H^\infty into the Zygmund Spaces

In this work we characterize the bounded and the compact weighted composition operators from the space $H^\infty $ of bounded analytic functions on the open unit disk into the Zygmund space and the little Zygmund space. We also provide boundedness and compactness criteria of the weighted composition operators from the Bloch space into the little Zygmund space. In particular, we show that the bounded operators between these spaces are necessarily compact.     

Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space

Let ${{\varphi}}$ be an analytic self-map of the open unit disk ${{\mathbb{D}}}$ in the complex plane ${{\mathbb{C}, H(\mathbb{D})}}$ the space of complex-valued analytic functions on ${{\mathbb{D}}}$ , and let u be a fixed function in ${{H(\mathbb{D})}}$ . The weighted composition operator is defined by $$(uC_{\varphi}f)(z) = u(z)f({\varphi}(z)), \quad z \in \mathbb{D}, f \in H(\mathbb{D}).$$ In this paper, we study the boundedness and the compactness of the weighted composition operators from the minimal Möbius invariant space into the Bloch space and the little Bloch space.     

GENERALIZED HILBERT OPERATOR AND FEJ(E)R-RIESZ TYPE INEQUALITIES ON THE POLYDISC

Let ∫ be a holomorphic function on the unit polydisc Dn, with Taylor expansion ∫(z)= ∞∑|k|=0αkzk(=)∞∑k1+…+kn=0 αk1, …,knZk11…Zknn where k=(k1,…, kn)∈Zn+. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z)=∞ ∑|k|=0i1,…in≥0αi1,…,inn∏j=1Γ(γj+kj+1) Γ(kj+ij+1)/Γ(kj+1) Γ(kj+ij+γj+2)zk,where γ∈Cn, such that Rγj -1,j = 1,2,…,n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type inequality on the weighted Bergman space on Dn and find an invariant space for the generalized Hilbert operator.     

Generalized Hilbert operator on the Dirichlet-type space

The boundedness of the generalized Hilbert operator on the Dirichlet-type space S_p when 0<p<1 is investigated.     

A class of integral operators on mixed norm spaces in the unit ball

This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball. The author is supported in part by the NNSF China (No. 10671115), grants from Specialized Research Fund for the doctoral program of Higher Education (No. 20060560002) and NSF of Guangdong Province (No. 06105468).     

Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces

The boundedness and compactness of the products of differentiation and composition operators from Zygmund spaces to Bloch spaces and Bers spaces are discussed in this paper.     

Differences of generalized composition operators on the Bloch space

The boundedness and compactness of the differences of two generalized composition operators on the Bloch space in the unit disk are investigated in this paper.     

Weighted composition operators from Bergman-type spaces into Bloch spaces

Let ϕ be an analytic self-map and u be a fixed analytic function on the open unit disk D in the complex plane ℂ. The weighted composition operator is defined by

Riemann–Stieltjes operators between α ‐Bloch spaces and Besov spaces

We study the following two integral operators where g is an analytic function on the open unit disk in the complex plane. The boundedness and compactness of these two operators between the α ‐Bloch space B^α and the Besov space are discussed in this paper (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)