and Applied Analysis 3 Let D be the differentiation operator on H D , that is, Df z f ′ z . For f ∈ H D , the products of composition and differentiation operators DCφ and CφD are defined, respectively, by DCφ ( f ) ( f ◦ φ)′ f ′(φ) φ′, CφD ( f ) f ′ ( φ ) , f ∈ H D . 1.8 The boundedness and compactness of DCφ on the Hardy space were investigated by Hibschweiler and Portnoy in 11 and by Ohno in...

Composition of fuzzy operators often appears and it is natural to ask when the order of composition does not change the result. In previous papers, we characterized permutability in the case of fuzzy consequence operators and fuzzy interior operators. We also showed the connection between the permutability of the fuzzy relations and the permutability of their induced fuzzy operators. In this wo...

The boundedness of the weighted differentiation composition operator from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (zn)n∈N0 . An asymptotic estimate of the essential norm of the operator is also given in terms of the sequence, which gives a characterization for the compactness of the operator.

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

Let 1 ≤ p < ∞ and let μ be a positive finite Borel measure on the unit disk D. The area Nevanlinna-Lebesgue space Np(μ) consists of all measurable functions h on D such that log |h| ∈ Lp(μ), and the area Nevanlinna space N α is the subspace of N p((1 − |z|2)αdν(z)), where α > −1 and ν is area measure on D, consisting of all holomorphic functions. We characterize Carleson measures for N α, defin...

We study the boundedness and compactness of the differences of two weighted composition operators acting from the Bloch space B to the space H∞ of bounded analytic functions on the open unit disk. Such a study has a relationship to the topological structure problem of composition operators on H∞. Using this relation, we will estimate the operator norms and the essential norms of the differences...

* Correspondence: [email protected] Department of Mathematics, Tianjin University, Tianjin, 300072 People’s Republic of China Abstract In this paper, we investigate the compactness of the sum of weighted composition operators on the unit ball algebra, and give the characterization of compact differences of two weighted composition operators on the ball algebra. The connectness of the t...

We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Blo...

We study the questions of the composition of operators which can not be answered by using the properties of each operator separately. Phong and Stein studied the week type (1, 1) estimate while Han et al. considered the Hardy space for the composition of operators with different homogeneities. In this paper, we characterize a class of the Muckenhoupt Ap weights associated with different homogen...