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Let φ denote a nonconstant analytic self-map of the open unit disk D, g be an analytic function on D. In this paper, we characterize the necessary or sufficient conditions for generalized composition operators Cgφ f(z) = ∫ z 0 f'(φ(ξ))g(ξ)dξ, on the Bloch-type spaces to have a closed range. Moreover, if g ∊ H∞, according to relationship betweenα and β, we show several conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we use Young's function to define Zygmund-Orlicz space. We study boundedness and compactness of composition operator on Zygmund-Orlicz space. [ABSTRACT FROM AUTHOR]

In this paper, we use Young's function to define Zygmund-Orlicz space. We study boundedness and compactness of composition operator on Zygmund-Orlicz space. [ABSTRACT FROM AUTHOR]

We characterize when N-tuples Br1a1, ⋯, BrNaNof powers of unilateral weighted back-ward shift operators defined the space of all complex valued square summable sequences exhibit the d-mixing properties, and give several equivalent conditions of d-mixing properties. At the same time, d-mixing powers of bilateral weighted backward shifts on Banach sequence spaces are also discussed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the isometries of the products of composition and differentiation operators from the Bloch type space to the space of all weighted bounded analytic functions in the disk. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the isometries of the products of composition and differentiation operators from the Bloch type space to the space of all weighted bounded analytic functions in the disk. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the boundedness and compactness of the product of extended Cesàro operator and composition operator from the logarithmic Bloch-type space to F(p, q, s) space on the unit ball of ℂn. [ABSTRACT FROM AUTHOR]

In 1987, Shapiro showed that composition operator induced by symbol φ is compact on the Lipschitz space if and only if the infinity norm of φ is less than 1 by a spectral-theoretic argument, where φ is a holomorphic self-map of the unit disk. In this note, we shall generalize Shapiro's result to the n-dimensional case. [ABSTRACT FROM AUTHOR]

In 1987, Shapiro showed that composition operator induced by symbol φ is compact on the Lipschitz space if and only if the infinity norm of φ is less than 1 by a spectral-theoretic argument, where φ is a holomorphic self-map of the unit disk. In this note, we shall generalize Shapiro's result to the n-dimensional case. [ABSTRACT FROM AUTHOR]

In this paper, we characterize nth differentiation composition operators from weighted Banach space of holomorphic function to weighted Bloch space, and give some necessary and sufficient conditions for the boundedness and compactness of the operators. [ABSTRACT FROM AUTHOR]