Bloch-type Spaces Research Articles

The composition type operator on the weighted Bergman space in the unit ball

In this paper, the briefly necessary and sufficient conditions are given for the weighted composition operator Tψ,φ to be bounded (or compact) from the weighted Bergman space Aαp to the Bloch type space βq on the unit ball in Cn. At the same time, the following results are given: (1) If composition operator Cφ is bounded on Aαp , then Cφ is a compact operator on Aαp if and only if lim| z |→1-[(1-| z |)/(1-| φ ( z )|)=0. The result improves Kehe Zhus corresponding result. (2) Composition operator Cφ is a compact operator from Aαp to β n +1+ α + p / p if and only if lim| z |→1-[(1-| z |)/(1-| φ ( z )|)]=0.

Function Spaces and Applications

Function spaces and its various applications are subjects of investigation in many research centers and we are glad that this special issue has received the remarkable attention by researchers in these areas. We have received papers from wide range of topics of function spaces such as interpolation methods for stochastic processes spaces, vector optimization problems in Banach spaces, Marcinkiewicz integral operator in Morrey spaces, Hardy’s operator in the variable exponent Lebesgue spaces, and differential equations of weakly parabolic type in Banach spaces. A number of papers are devoted to investigating different kinds of problems in Hardy spaces or Hardy subspaces, for example, Calderon-Zygumnd singular integral operators in Hardy spaces, weighted Hardy spaces related to the Schrodinger operator, and composition operator in hyperbolic Bloch-type spaces. Geometric problems such as modulus of convexity in some Banach sequence spaces, p-uniform convexity, and quniform smoothness in C spaces are also covered by this issue.

New characterizations for the products of differentiation and composition operators between Bloch-type spaces

We use a brief way to give various equivalent characterizations for the boundedness and the essential norm of the operator acting on Bloch-type spaces. At the same time, we use this method to easily get a known characterization for the operator on Bloch-type spaces. MSC:47B38, 26A24, 32H02, 47B33.

New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk

AbstractWe give some new characterizations for compactness of weighted composition operators uCφ acting on Bloch-type spaces in terms of the power of the components of φ where φ is a holomorphic self-map of the polydisk 𝔻n, thus generalizing the results obtained by Hyvärinen and Lindström in 2012.

THE WEIGHTED POINCARÉ DISTANCE IN THE HALF PLANE

In this paper we introduce the weighted Poincaré distance and the induced distance by the weighted Bloch type space. We prove that the weighted Poincaré distance is identical to the inner distance generated by the induced distance.

Essential norms of generalized composition operators between Bloch-type spaces in the unit ball

Let be the class of all holomorphic functions on the unit ball in . For with and an analytic self-map of , the generalized composition operator is defined byIn this paper, we give estimates for the essential norms of the generalized composition operators between Bloch-type spaces in terms of the powers of the components of . We also give new characterizations for the boundedness and compactness of between Bloch-type spaces.

On characterizations of Bloch-type, Hardy-type and Lipschitz-type spaces

In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some applications to non-homogeneous Yukawa PDEs. We also consider some properties of the Lipschitz-type spaces on certain classes of complex-valued functions. Finally, we will study a class of composition operators on these spaces.

Essential Norms of Weighted Composition Operators from Bloch-Type Space to $$H^\infty $$ H ∞ on the Unit Ball

In this paper, we express the essential norm of a weighted composition operator from a Bloch-type space to $$H^\infty $$ on the unit ball. Moreover, we obtain the parallel results for the weighted composition operator which acts from the Bloch-type space to a weighted-type space.

TOEPLITZ OPERATORS ON BLOCH-TYPE SPACES AND A GENERALIZATION OF BLOCH-TYPE SPACES

We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of <TEX>${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$</TEX> on the boundary of <TEX>$\mathbb{D}$</TEX> implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

Weighted composition followed and proceeded by differentiation operators fromZygmund spaces to Bloch-type spaces

In this paper, we investigate boundedness and compactness of the weighted composition followed and proceeded by differentiation operators from Qk(p, q) spaces to Bloch-type spaces and little Bloch-type spaces. Some sufficient and necessary conditions for the boundedness and compactness of these operators are obtained. MSC: 47B38; 30D45

On generalized superposition operator acting of analytic function spaces

Abstract In this paper we introduce a new integration operator S g , ϕ ( n ) , where S g , ϕ ( n ) = ∫ 0 z ϕ ( n ) ( f ( ξ ) ) g ( ξ ) d ξ . We characterize all entire functions that transform a Bloch-type space into another by this new integration operator. Also, we prove that all generalized superposition operators induced by such entire functions are bounded.

Random Harmonic Functions in Growth Spaces and Bloch-type Spaces

Abstract. Let h∞v (D) and h∞v (B) be the spaces of harmonic functions in the unit disk and multidimensional unit ball admitting a two-sided radial majorant v(r). We consider functions v that fulfill a doubling condition. In the two-dimensional case letwhere ξ ={ξji} is a sequence of random subnormal variables and aji are real. In higher dimensions we consider series of spherical harmonics. We will obtain conditions on the coefficients aji that imply that u is in h∞v (B) almost surely. Our estimate improves previous results by Bennett, Stegenga, and Timoney, and we prove that the estimate is sharp. The results for growth spaces can easily be applied to Bloch-type spaces, and we obtain a similar characterization for these spaces that generalizes results by Anderson, Clunie, and Pommerenke and by Guo and Liu.

Essential norms of the integral-type composition operators between Bloch-type spaces

In this paper, we give some new and simple characterizations for the boundedness and compactness of the integral-type composition operators acting on Bloch-type spaces, and obtain corresponding estimates for their essential norms in terms of the sequence . From which the sufficient and necessary conditions of compactness of the integral-type composition operators follows immediately.

Generalized weighted composition operators from Bers-type spaces into Bloch-type spaces

New criteria for the boundedness and the compactness of the generalized weighted composition operators from Bers-type spaces into Bloch-type spaces are given in this paper. Mathematics subject classification (2010): Primary 47B33, Secondary 30H30.

New estimate of essential norm of composition followed by differentiation between Bloch-type spaces

We give a new characterization for the boundedness of composi- tion operator followed by dierentiation operator acting on Bloch-type spaces and calculate its essential norm in terms of the n-th power of the induced an- alytic self-map on the unit disk. From which some sucient and necessary conditions of compactness of the operator follow immediately.

Differences of generalized composition operators between Bloch type spaces

Let φ and ψ be analytic self-maps of the open unit disk D . Using pseudo-hyperbolic distance ρ(φ ,ψ) , we characterize the boundedness and compactness of the differences of generalized composition operators (C φ −Ch ψ ) f (z) = ∫ z 0 [ f ′(φ(ξ ))g(ξ )− f ′(ψ(ξ ))h(ξ )]dξ , z ∈ D between two Bloch-type spaces on D . The results generalize the corresponding results on the single generalized composition operator and on the differences of generalized composition operators on the Bloch space. Mathematics subject classification (2010): Primary 47B38; secondary 30H30.

Distance from Bloch-Type Functions to the Analytic SpaceF(p,q,s)

The analytic spaceF(p,q,s)can be embedded into a Bloch-type space. We establish a distance formula from Bloch-type functions toF(p,q,s), which generalizes the distance formula from Bloch functions to BMOA by Peter Jones, and toF(p,p-2,s)by Zhao.

Essential norms of weighted composition operators between Zygmund-type spaces and Bloch-type spaces

We investigate the boundedness of weighted composition operator uC φ mapping the Zygmund-type space Zinto the Bloch-type space B � . Then we give essential norm estimates of such an operator in terms of u and φ.

Weighted Composition Operator from Mixed Norm Space to Bloch-Type Space on the Unit Ball

We discuss the boundedness and compactness of the weighted composition operator from mixed norm space to Bloch-type space on the unit ball ofCn.

Composition Operators Between Bloch Type Spaces in the Unit Ball

In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators ϕ between Bloch type spaces in the unit ball Bn.