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Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spaces Bω and Bω,0 to mixed-norm space H(p,q,φ) on the unit ball B .

This paper discusses the hypercyclicity of weighted composi- tion operators acting on the space of holomorphic functions on the open unit ball BN of CN. Several analytic properties of linear fractional self- maps of BN are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

Let E be a complex Banach space, with the unit ball BE. We study the spectrum of a bounded weighted composition operator uCφ on H∞(BE) determined by an analytic symbol φ with a fixed point in BE such that φ(BE) is a relatively compact subset of E, where u is an analytic function on BE.

In this paper, we investigate the connection between compactness of operators on the Bergman space and the boundary behaviour of the corresponding Berezin transform. We prove that for a class of operators that we call radial operators, an oscillation criterion and diagonal are sufficient conditions under which the compactness of an operator is equivalent to the vanishing of the Berezin transform on the unit sphere. We further study a special class of radial operators, i.e., Toeplitz operators with a radial L1(Bn) symbol.

N doped ZnO thin films were prepared by magnetron sputtering. The effect of bias voltage, N2flow and introducing of Al on the behavior of N doping into ZnO films were investigated. The results show that there is little help for N doping into the ZnO films by just adjusting N flow rate because the magnetron sputtering method has a relative weak ability on dissociating the N2. The data of co-doping of Al and N into ZnO films revealed that co-doping is an effective way to advance the N doping into ZnO films. The coordination of Al doping and bias voltage could help the N doping effectively.

This paper characterizes the boundedness and compactness of the product of extended Cesàro operator and composition operator from Lipschitz space toF(p,q,s)space on the unit ball ofℂn.

The synthesis of nanocrystalline pure anatase at low temperature and short time is not an easy achievement, as the synthetic processes generally lead to amorphous, moreover some processes normally require harsh reaction. Uniform nanocrystalline pure anatase has been obtained using tetrabutyl titanate and normal butyl alcohol under microwave irradiation condition at low temperature 120 °C for 3 h. This process simplication will lower production cost and make continuous process possible. It was revealed that the as-synthesized TiO2 products without any heat treatment were uniformly dispersed and granulous single-phase anatase, with the average grain size of 10 nm, by means of XRD and TEM.

Let ϕ and ψ be holomorphic self-maps of the unit disk, and denote by C ϕ , C ψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators C ϕ −C ψ from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.

For , let denote the -Bloch space on the unit polydisc of and a holomorphic self-map of . We investigate the boundedness and compactness of the weighted composition between -Bloch space (little -Bloch space ) and -Bloch space (little -Bloch space ). The most important result in the paper is that conditions for the compactness are different for the cases and , unlike for the case of the weighted operators on the unit disc. Bibliography: 32 titles.

Let g be a holomorphic map of B , where B is the unit ball of Cn . This paper gives necessary and sufficient conditions for the extended Cesaro operators induced by g to be bounded or compact on BMOA. Mathematics subject classification (2010): Primary: 47B38; Secondary: 46E15, 32A37..

In this paper, we first discuss some basic results concerning Toeplitz operators with quasihomogeneous symbols (i.e., symbols being of the form e ipθ ϕ, where ϕ is a radial function) on the harmonic Bergman space. Then we determine when the product of two Toeplitz operators with quasihomogeneous symbols is a Toeplitz operator.

Let g be a holomorphic function of the unit ball B in the n-dimensional complex space, and denote by T g the extended Cesaro operator with symbol g. Starting with a brief introduction to well-known results about Cesaro operator, we investigate the boundedness and compactness of T g from generally weighted Bloch spaces B log α ( 0 α ∞ ) to Zygmund space Z in the unit ball, and also present some necessary and sufficient conditions.

We investigate the adjoints of linear fractional composition operators C ϕ acting on classical Dirichlet space D(B N ) in the unit ball B N of ℂ N , and characterize the normality and essential normality of C ϕ on D(B N ) and the Dirichlet space modulo constant function D 0(B N ), where ϕ is a linear fractional map ϕ of B N . In addition, we also show that for any non-elliptic linear fractional map ϕ of B N , the composition maps σ o ϕ and ϕ o σ are elliptic or parabolic linear fractional maps of B N .

In this paper, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the unit ball in \({\mathbb{C}}^{n}\). We first determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. Next, we investigate the zero-product problem for several Toeplitz operators with radial symbols. Also, the corresponding commuting problem of Toeplitz operators whose symbols are of the form \(\xi^{k} \varphi\) is studied, where \(k \in {\mathbb{Z}}^{n}\) and φ is a radial function.

Let φ and ψ be holomorphic self-maps of the unit polydisc Un in the n-dimensional complex space, and denote by Cφ and Cψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators Cφ−Cψ from Bloch space to bounded holomorphic function space in the unit polydisc. The compactness of the difference is also characterized.

Let ϕ(z) = (ϕ1(z),…,ϕn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of ℂn. Let 0 < p, s < +∞, -n - 1 < q < +∞, q+s > -1 and α ≥ 0, this paper characterizes boundedness and compactness of weighted composition operator Wψ,ϕ induced by ϕ and ψ between the space F(p, q, s) and α-Bloch space [Formula: see text].

This paper gives some estimates of the essential norm for the difference of composition operators induced byφandψacting on the space,H∞(Dn), of bounded analytic functions on the unit polydiscDn, whereφandψare holomorphic self-maps ofDn. As a consequence, one obtains conditions in terms of the Carathéodory distance onDnthat characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators onH∞(Dn)is compact.

We characterize the disjoint supercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces l2(N,w), c0(N,w) , and l2(Z,w), c0(Z,w), where w=(wi)i is a positive weight sequence satisfying wi \geq 1 for every i\in N (or i\in Z).

The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous. Motivated by those, we investigate conditions to ensure that finite many powers of differentiation operators are disjoint hypercyclic on generalized weighted Bergman spaces of entire functions.

In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the composition operator to be compact on the Bloch space in a bounded symmetric domain.

Let Un be the unit polydisc of ℂn and φ = ( φ 1 , * , φ n ) a holomorphic self-map of Un. This paper shows that the composition operator C φ induced by φ is bounded on the little Bloch space β 0 * ( U n ) if and only if φ l ∈ β 0 * ( U n ) for every l = 1 , 2 , * , n , and also gives a sufficient and necessary condition for the composition operator C φ to be compact on the little Bloch space β 0 * ( U n ) .

Let Bn be the unit ball of C n and o = o1 … o n a holomorphic self-map of B n . The main purpose of this paper is to discuss the boundedness and compactness of composition operator Co between p-Bloch space βp Bn and q-Bloch space βqBn … wherep p ⩾0 and q⩾0.

Let $S(\mathbb{D})$ be the collection of all the holomorphic self-maps of open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$, and $C_{\varphi}$, the composition operator induced by $\varphi\in S(\mathbb{D})$. For $\alpha>0,\;\lambda\in \mathbb{C}$, we give some sufficient and necessary conditions for the hypercyclicity of multiples of composition operators $\lambda C_\varphi$ acting on the weighted Banach spaces of entire functions $H_{\alpha,0}^\infty$. Moreover, we obtain a partial characterization for the frequent hypercyclicity of $\lambda C_\varphi$ on $H_{\alpha,0}^\infty$.

We study the ranks of commutators and generalized semicommutators of Toeplitz operators with quasihomogeneous symbols on both the harmonic Bergman space and the Bergman Space. In particular, when one of quasihomogeneous symbols is the the form of $e^{ik\theta }r^{m}$, we first obtain specific sufficient and necessary conditions for commutators and generalized semicommutators to be finite rank. Then we make further efforts to determine the range of each finite rank commutator and generalized semicommutators, and consequently the explicit canonical form and the rank are obtained. Thus, the finite rank problem of commutators and generalized semicommutators of such special Toeplitz operators is completely solved. As applications, several interesting corollaries and nontrivial examples are given. Also, we show close connections of the finite rank problem between the harmonic Bergman space and Bergman space cases., Comment: 29 pages

We study the topological structure of the space of all bounded composition operators from $F(p,q,s)$ to $\mathcal{B}_\mu$ on the unit disk $\mathbb{D}$ in the operator norm topology. At the same time, we characterizes the boundedness and compactness of the differences of two composition operators.

The image is a kind of important information source, through the image processing can help people understand the connotation of the information. However, the image in the process of generation and transmission by all kinds of the noise, the information processing, transfer and storage caused tremendous influence. So the image denoising always all is the computer image processing and computer in the vision of a research focus. Proposed an algorithm of image denoising based on the local structural similarity. Which utilizes the redundant information, and by establishing a similar function to the search area calculation of point and to pixels similarity of weights, and then to the search area at the weighted, obtained the last to pixels gray value varies. This algorithm in texture, of the edge information denoising ways than the current many denoising algorithm are excellent.

This paper characterizes the boundedness and compactness of the product of extended Cesàro operator and composition operator from Lipschitz space to $F(p,q,s)$ space on the unit ball of ${\mathbb{C}}^{n}$ .

Let 𝑔 be a holomorphic of the unit ballBin then-dimensional complex space, and denote byTgthe extended Cesáro operator with symbolg. Let 0 −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness ofTgbetween generalized Besov spaceB(p, q)and 𝛼α- Bloch spaceℬαin the unit ball, and also present some necessary and sufficient conditions.

Bemisia tabaci, a pest insect with stronger capabilities of flying and host plant-exploitation, is capable of flying 150 m high and over a distance as far as 7 km, but hardly flies higher than 0. 5 m and long distance in food-abundant areas. B. tabaci has the characteristics of both searching-and migrating flying, which enable it to exploit and locate on suitable hosts. Up to now, no oogenesis-flight syndrome of B. tabaci has been detected. Visual spectrum, air temperature and relative humidity, host quality, and wind speed are the main factors affecting the flight behavior of B. tabaci. In this paper, the flying capability of B. tabaci and the factors affecting its flight behavior were summarized, and the corresponding IPM strategies in the areas where B. tabaci could not overwintering in open field were discussed.

Titanium dioxide of the rutile phase has been synthesized using titanium tetrachloride and hydrochloric acid by means of microwave hydrothermal method. The mixture solution is processed in microwave hydrothermal autoclave first at 120 °C for 1.5 h and then at 180 °C for 1 h to precipitate rutile powders. It was revealed that well-dispersed and shuttle-like rutile TiO2 with the average diameter of 10 nm was formed by means of XRD and TEM.

Nanocrystalline titanium dioxide was synthesized by microwave hydrothermal (MH) using tetrabutyl titanate and normal butyl alcohol as start materials. The mixture solution of tetrabutyl titanate and normal butyl alcohol in 1:1.5 molar ratio was processed in a microwave hydrothermal digestion system at 200oC for 20 min to prepare nanosized TiO2 powders. The results showed that the microwave assisted reactions proceed at a faster rate than the traditional hydrothermal methods. The powder was heat treated at 500oC and the final products is ~20 nm in size and well dispersed.

Let Un be the unit polydisc of Cn and φ = (φ1,...,φn) a holomorphic self-map of Un. Let 0 ≤α 1. This paper shows that the composition operator C is bounded on the Lipschitz space Lip(Un) if and only if there exists M > 0 such that $$\sum\limits_{k,l = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial zk}}(z)} \right|\left( {\frac{{1 - \left| {z_k } \right|^2 }}{{1 - \left| {\phi _l (z)} \right|^2 }}} \right)^{1 - \alpha } } \leqslant M$$ for z ∈ Un. Moreover Cφ is compact on Lipα(Un) if and only if Cφ is bounded on Lipα(Un) and for every e>0, there exists a δ > 0 such that $$\sum\limits_{k,l = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial zk}}(z)} \right|\left( {\frac{{1 - \left| {z_k } \right|^2 }}{{1 - \left| {\phi _l (z)} \right|^2 }}} \right)^{1 - \alpha } } \leqslant \varepsilon $$ whenever dist((z),∂Un).