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In this paper, we study the boundedness and compactness of the inclusion mapping from Besov spaces to tent spaces. Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators from Besov spaces to general function spaces are also investigated.

In this paper, we study the boundedness and compactness of the Volterra integral operators from Dirichlet type spaces $${\mathcal {D}}^p_{p-2+s}$$ into Hardy spaces $${\mathcal {H}}^q$$ when $$1

A class of Dirichlet-Morrey spaces $ D_{\beta, \lambda} $ is introduced in this paper. For any positive Borel measure $ \mu $, the boundedness and compactness of the identity operator from $ D_{\beta, \lambda} $ into the tent space $ \mathcal{T}_s^1(\mu) $ are characterized. As an application, the boundedness of the Volterra integral operator $ T_g: D_{\beta, \lambda} \to F(1, \beta-s, s) $ is studied. Moreover, the essential norm and the compactness of the operator $ T_g $ are also investigated.

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi $ on Bergman type spaces $A_\omega ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_\varphi \colon A_\omega ^p\to A_\omega ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^\infty $ if and only if ϕ is a finite Blaschke product.

Some new characterizations for the boundedness and compactness of the difference of two weighted composition operators acting from $$H^\infty $$ to the Bloch space are given in this paper.

In this paper, we study the boundedness and compactness of the identity operator $$I:BMOA_{\log }\rightarrow \mathcal {T}^{\infty }_{\log }(\mu )$$. As applications, we characterize the boundedness and compactness of the Volterra integral operators $$T_g$$ and $$I_g$$ on the space $$BMOA_{\log }$$. The estimations for the essential norm of $$T_g$$ and $$I_g$$ on the space $$BMOA_{\log }$$ are also given.

In this paper, we give some estimates for the essential norm of weighted composition operators from analytic Besov spaces into Zygmund type spaces. In particular, a new characterization for the boundedness and compactness of the weighted composition operators uCϕ is obtained.

In this paper, we characterize the closures of Dirichlet type spaces D α in the logarithmic Bloch space. Moreover, we study the boundedness and compactness of composition operators from the logarithmic Bloch space to closures of Dirichlet type spaces D α in the logarithmic Bloch space.

The boundedness, compactness and essential norm of weighted composition operators from H∞ to the Bloch space in the unit ball of Cn are investigated in this paper. In particular, some new character...

We characterize the closure of Dirichlet type spaces Dμ in Bloch type spaces. Moreover, we study the boundedness and compactness of composition operators from Bloch type spaces to closures of Dirichlet type spaces Dμ in Bloch type spaces.

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.

In this paper, we give some new essential norm estimates of weighted composition operators \(uC_{\varphi }\) from analytic Besov spaces into the Bloch space, where u is a function analytic on the unit disk \(\mathbb {D}\) and \(\varphi \) is an analytic self-map of \(\mathbb {D}\). Moreover, new characterizations for the boundedness, compactness and essential norm of weighted composition operators \(uC_{\varphi }\) are obtained by the nth power of the symbol \(\varphi \) and the Volterra operators \(I_u\) and \(J_u\).

In this work, the boundedness of the weighted composition operator $$uC_\varphi $$ from $$H^\infty $$ to nth weighted type spaces was characterized. Also some estimates for the essential norm of this operator were given. By applying these estimates for the essential norm, some necessary and sufficient conditions for the compactness of this operator were obtained.

In this paper, we give three different characterizations for the boundedness and compactness of composition operators between different weighted Dirichlet spaces in the unit disk.

The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the A 2 theorem for Calderon-Zygmund operators in harmonic analysis. Using this tool from harmonic analysis, some new characterizations are given for the boundedness and compactness of weighted composition operators acting between weighted Bergman spaces in the upper half plane. Moreover, we establish a new weighted type estimate for the holomorphic Bergman-class functions, for a new class of weights, which is adapted to Sawyer–testing conditions. We also extend our results to the unit ball B in C n .

We study the boundedness and compactness of the differences of two generalized weighted composition operators acting from the Bloch space to Bers-type spaces.

In this paper, we study the boundedness, compactness and essential norm of differences of composition operators \(C_{\varphi }-C_{\psi }\) on Bloch type spaces. In particular, we use the Bloch type norm of \(\varphi ^n-\psi ^n\) to characterize these.

In this paper, we give new essential norm estimates of weighted composition operators from into the Bloch space, where u is a function analytic on the unit disc and is an analytic self-map of . Moreover, a new characterization for the boundedness and compactness of the weighted composition operators is obtained by the nth power of the symbol and the Volterra operators and .

Let $ \mu $ be a positive Borel measure on the interval $ [0, 1) $. The Hankel matrix $ {\mathcal H}_\mu = (\mu_{n+k})_{n, k\geq 0} $ with entries $ \mu_{n, k} = \mu_{n+k} $ induces the operator $ {\mathcal H}_\mu(f)(z) = \sum\limits_{n = 0}^\infty\left(\sum\limits_{k = 0}^\infty\mu_{n,k}a_k\right)z^n $ on the space of all analytic functions $ f(z) = \sum^\infty_{n = 0}a_nz^n $ in the unit disk $ {\mathbb{D}} $. In this paper, we characterize the boundedness and compactness of $ {\mathcal H}_\mu $ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $ {\mathcal H}_\mu $ from $ {\mathcal{B}}^\alpha $ to $ {\mathcal{B}} $ and BMOA.

In this paper, a new characterization is provided for the boundedness, compactness and essential norm of the difference of two weighted composition operators on weighted-type spaces in the unit ball of $\mathbb{C}^n$.

We give some new estimates for the essential norm of weighted composition operators on the space $\mathit{BMOA}$ . As a corollary, we obtain a new characterization for the compactness of weighted composition operators on the space $\mathit{BMOA}$ .

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.

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.

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 Mobius invariant space into the Bloch space and the little Bloch space.

Let n be a positive integer, 1 ? H(D) and ? be an analytic self-map of D. The boundedness and compactness of the integral operator (Cn ?,1 f )(z) = ?z 0 f (n)(?(?))1(?)d? from the Bloch and little Bloch space into the spaces QK(p, q) and QK,0(p, q) are characterized.

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.

Let H(B) denote the space of all holomorphic functions on the unit ball B@?C^n. We study the boundedness and compactness of the following integral-type operatorP"g(f)(z)=@!"0^1f(tz)g(tz)dtt,f@?H(B),z@?B,where g@?H(B) and g(0)=0, from @w-Bloch spaces to @m-Zygmund spaces.

Let H(B) denote the space of all holomorphic functions on the open unit ball B of C^n. Let @f=(@f"1,...,@f"n) be a holomorphic self-map of B and [email protected]?H(B) such that g(0)=0. In this paper we study the boundedness and compactness of the following integral-type operator, recently introduced by Xiangling Zhu and the second authorI"@f^gf(z)[email protected]!"0^1Rf(@f(tz))g(tz)dtt,[email protected]?B,from the iterated logarithmic Bloch spaces into the Bloch-type spaces. For the case when @f(z)=z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic Bloch space into the little Bloch-type space.

Let H(B) denote the space of all holomorphic functions on the unit ball [email protected]?C^n. This paper investigates the following integral-type operator with symbol [email protected]?H(B)T"g(f)(z)[email protected]!"0^1f(tz)Rg(tz)dtt,[email protected]?H(B),[email protected]?B,where Rg(z)[email protected]?"j"="1^nz"[email protected][email protected]?z"j(z) is the radial derivative of g. The boundedness and compactness of the operator T"g from Bloch-type spaces to Zygmund-type spaces are studied.

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 Bα and the Besov space are discussed in this paper (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Let H ( B ) denote the space of all holomorphic functions on the unit ball B ⊂ C n . In this paper we investigate the following integral operators: T g ( f ) ( z ) = ∫ 0 1 f ( tz ) R g ( tz ) dt t and L g ( f ) ( z ) = ∫ 0 1 R f ( tz ) g ( tz ) dt t , where f ∈ H ( B ) , z ∈ B , g ∈ H ( B ) and R h ( z ) = ∑ j = 1 n z j ∂ h ∂ z j ( z ) is the radial derivative of h . The operator T g can be considered as an extension of the Cesaro operator on the unit disk. The boundedness and compactness of the operators T g and L g , on the Zygmund space and from the Zygmund space to the Bloch space are studied.

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 ( uC φ ) ( f ) ( z ) = u ( z ) f ( φ ( z ) ) , z ∈ D , f ∈ H ( D ) . This paper studies the boundedness and compactness of weighted composition operators from Zygmund spaces into Bloch spaces.

The boundedness and compactness of the products of Volterra type operators and composition operators from the space of bounded analytic functions and the Bloch space to the Zygmund space are discussed in this paper.

The boundedness and compactness of the generalized composition operator on Zygmund spaces and Bloch type spaces are investigated in this paper.

Let n be the unit polydisc of ℂn, ϕ(z) = (ϕ1(z),…, ϕn(z)) be a holomorphic self-map of n, and ψ(z) a holomorphic function on n. Let H∞(n) be the space of all bounded holomorphic functions on n and ℬα(n) the α-Bloch space. Necessary and sufficient conditions for the weighted composition operator ψCϕ induced by ϕ(z) and ψ(z) to be bounded and compact from ℬα(n) to H∞(n) are given in this paper. One of our results corrects and extends Theorem 1 in the paper by S. Ohno, Weighted composition operators between H∞ and the Bloch space, Taiwanese J. Math. 2001; 5:555–563.

Suppose that ϕ is a nonconstant analytic self-map of the unit disk D. Compactness of composition operator C ϕ between two Mobius spaces Q K 1 and Q K 2 is studied. Moreover, necessary and sufficient condition for C ϕ from the Dirichlet space D to a general class of analytic functions F ( p , q , s ) to be compact is given in terms of the map ϕ.

The boundedness and the compactness of the two integral operators ; , where is an analytic function on the open unit disk in the complex plane, on the Zygmund space are studied.

Some criteria for the boundedness, as well as for the compactness, of the generalized weighted composition operator $D^{n}_{\varphi, u}$ from α-Bloch spaces into weighted-type spaces are given. Estimates for the norm and the essential norm of the operator are also given. Our results extend and complement some results in the literature.

The boundedness and compactness of composition operators from Zygmund and little Zygmund spaces into QK and QK,0 spaces are characterized in this paper. MSC: Primary 47B33; secondary 30H99

We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.

The logarithmic Bloch spaceBlog⁡is the Banach space of analytic functions on the open unit disk𝔻whose elementsfsatisfy the condition∥f∥=sup⁡z∈𝔻(1-|z|2)log⁡ (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceHp(with1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingHpinto the little logarithmic Bloch space defined as the subspace ofBlog⁡consisting of the functionsfsuch thatlim⁡|z|→1(1-|z|2)log⁡ (2/(1-|z|2))|f'(z)|=0.

Let $g:B\to \mathbb C^1$ be a holomorphic map of the unit ball $B$. We give a complete picture regarding the boundedness and compactness of the following two integral operators $$ T_gf(z)=\int_0^1f(tz)\Re g(tz)\frac{dt}{t}\text{ and } L_gf(z)= \int_0^1 \Re f(tz) g(tz)\frac{dt}{t},\quad z\in B, $$ between different weighted Bergman spaces.

Let $g:B\to \mathbb C^1$ be a holomorphic map of the unit ball $B$. We study the integral operators $$ T_gf(z)=\int_0^1f(tz)\Re g(tz)\frac{dt}{t}; \ \ L_gf(z)= \int_0^1 \Re f(tz) g(tz)\frac{dt}{t},\qquad z\in B. $$ The boundedness and compactness of the operators $T_g$ and $L_g$ on the Hardy space $H^2$ in the unit ball are discussed in this paper.

We study the following integral operators:Jgf(z)=∫0zf(ξ)g′(ξ)dξ;Igf(z)=∫0zf′(ξ)g(ξ)dξ, wheregis an analytic function on the open unit disk in the complex plane. The boundedness and compactness ofJg,Igbetween the Bergman-type spaces and theα-Bloch spaces are investigated.

A complete picture on the boundedness and compactness of the products of integral-type operators and composition operators between Bloch-type spaces of holomorphic functions on the unit disk is given in this paper.