Weighted Differentiation Composition Operators Research Articles

On sum of weighted differentiation composition operators from Bergman spaces with admissible weights to Zygmund type spaces

On sum of weighted differentiation composition operators from Bergman spaces with admissible weights to Zygmund type spaces

N-th Derivative Hardy Spaces and Weighted Differentiation Composition Operators

n-th Derivative Hardy Spaces and Weighted Differentiation Composition Operators

Essential norm of weighted differentiation composition operators on Bergman spaces with admissible weights

Essential norm of weighted differentiation composition operators on Bergman spaces with admissible weights

Sums of weighted differentiation composition operators from weighted Bergman spaces to weighted Zygmund and Bloch-type spaces

Sums of weighted differentiation composition operators from weighted Bergman spaces to weighted Zygmund and Bloch-type spaces

Essential Norm of Integral Type Operators Mapping into Certain Banach Spaces of Analytic Functions

We study certain integral type operators acting on a large class of Banach spaces of analytic functions on the open unit disc. The operators map into weighted Banach spaces of analytic functions, Bloch type spaces or Zygmund type spaces. Besides characterizing boundedness, we give essential norm estimates of these operators. In order to investigate these operators, we also study weighted differentiation composition operators between these spaces.

Sums of Weighted Differentiation Composition Operators

We solve an interpolation problem in $$A^p_\alpha $$ involving specifying a set of (possibly not distinct) n points, where the $$k{\text {th}}$$ derivative at the $$k{\text {th}}$$ point is up to a constant as large as possible for functions of unit norm. The solution obtained has norm bounded by a constant independent of the points chosen. As a direct application, we obtain a characterization of the order-boundedness of a sum of products of weighted composition and differentiation operators acting between weighted Bergman spaces. We also characterize the compactness of such operators that map a weighted Bergman space into the space of bounded analytic functions.

Differences of weighted differentiation composition operators from α-Bloch space to H∞ space

This paper characterizes the boundedness and compactness of the differences of weighted differentiation composition operators acting from the ?-Bloch space B? to the space H? of bounded holomorphic functions on the unit disk D.

Essential norm of the weighted differentiation composition operator between Bloch-type spaces

Essential norm of the weighted differentiation composition operator between Bloch-type spaces

Weighted Differentiation Composition Operators Between Normal Weight Zygmund Spaces and Bloch Spaces in the Unit Ball of $$\hbox {C}^{\mathrm{n}}$$ C n for $$\hbox {n}>1$$ n > 1

Let \(\mu \) be a normal functions on [0, 1), and H(B) be the space of all holomorphic functions on the unit ball B of \(\mathbf C^{n}\). Let \(\varphi \) be a nonconstant holomorphic self-map on B, and \(\psi \) be a holomorphic function on B. The weighted differentiation composition operator \(\psi D_{\varphi }\) is defined on the space H(B) by \(\psi D_{\varphi }(f)=\psi (Rf)\circ \varphi \), for all \(f\in H(B)\). In this paper, the authors characterize the boundedness and compactness of the weighted differentiation composition operator \(\psi D_{\varphi }\) from the normal weight Zygmund space \(Z_{\mu }(B)\) to the normal weight Bloch space \(\beta _{\mu }(B)\) for \(n>1\). As a consequence of the main results, the authors give the briefly sufficient and necessary conditions that the differentiation composition operator \( D_{\varphi }\) is compact from \(Z_{\mu }(B)\) to \(\beta _{\mu }(B)\) for \(\displaystyle {\mu (r)=(1-r)^{s}\log ^{t}\frac{e}{1-r}}\).

New characterizations for differences of weighted differentiation composition operators from a Bloch-type space to a weighted-type space

We found several new equivalent characterizations of the boundedness of the differences of weighted differentiation composition operators from Bloch-type spaces to weighted-type spaces. Especially, we estimated its essential norm in terms of the n-th power of the induced analytic self-maps on the unit disk, which can provide a new and simple compactness criterion. Moreover, we applied our results to a classical example.

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

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space

Abstract The boundedness of the weighted differentiation composition opera- tor 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.

Differences of the Weighted Differentiation Composition Operators from Mixed-Norm Spaces to Weighted-Type Spaces

We characterize the boundedness and compactness of the differences of weighted differentiation composition operators $$ {D}_{\varphi_1,{u}_1}^n-{D}_{\varphi_2,{u}_2}^n, $$ where n ∈ ℕ0, u1,u2 ∈ H( $$ \mathbb{D} $$ ), and $$ \varphi $$ 1, $$ \varphi $$ 2 2 S( $$ \mathbb{D} $$ ), from mixed-norm spaces H(p, q, ϕ), where 0 < p, q < ∞ and ϕ is normal, to weighted-type spaces H ∞ .

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.

Weighted Differentiation Composition Operators to Bloch-Type Spaces

We characterized the boundedness and compactness of weighted differentiation composition operators from BMOA and the Bloch space to Bloch-type spaces. Moreover, we obtain new characterizations of boundedness and compactness of weighted differentiation composition operators.

Weighted differentiation composition operators from weighted bergman space to n th weighted space on the unit disk

This paper characterizes the boundedness and compactness of the weighted differentiation composition operator from weighted Bergman space to n th weighted space on the unit disk of ≤.2000 Mathematics Subject Classification: Primary: 47B38; Secondary: 32A37, 32H02, 47G10, 47B33.

Weighted differentiation composition operators from H ∞ to Zygmund spaces

Let ϕ be an analytic self-map of the unit disk 𝔻, H(𝔻) the space of analytic functions on 𝔻 and u∈H(𝔻). The boundedness and compactness of the weighted differentiation composition operator , where n∈ℕ0, from H ∞ to Zygmund space are investigated in this paper.

Weighted Differentiation Composition Operators from Mixed-Norm to Zygmund Spaces

Let ϕ be an analytic self-map of the unit disk 𝔻, H(𝔻) the space of analytic functions on 𝔻 and u ∈ H(𝔻). The boundedness and compactness of the weighted differentiation composition operator , where n ∈ ℕ0, from mixed-norm space to the Zygmund spaces, and the little Zygmund spaces are investigated in this article.

Weighted differentiation composition operators from H∞ and Bloch spaces to nth weighted-type spaces on the unit disk

We characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions, the Bloch space and the little Bloch space to nth weighted-type spaces on the unit disk.

Weighted Differentiation Composition Operators from the Mixed-Norm Space to the th Weigthed-Type Space on the Unit Disk

and Applied Analysis 3 2. Auxiliary Results Here we quote some auxiliary results which will be used in the proofs of the main results. The first lemma can be proved in a standard way see, e.g., in 13, Proposition 3.11 or in 15, Lemma 3 . Lemma 2.1. Assume that m ∈ N0, n ∈ N, p, q > 0, γ > −1, φ is an analytic self-map of D and u ∈ H D . Then the operator D φ,u : Hp,q,γ → W n μ is compact if and only if D φ,u : Hp,q,γ → W n μ is bounded and for any bounded sequence fk k∈N in Hp,q,γ which converges to zero uniformly on compact subsets of D, D φ,ufk → 0 inW n μ as k → ∞. The next lemma is known, but we give a proof of it for the benefit of the reader. Lemma 2.2. Assume that n ∈ N0, 0 −1 and m > 1 β one has ∫1 0 1 − r β ( 1 − ρrm ≤ C ( 1 − ρ) β−m, 0 0 and Dn a ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 1 1 · · · 1 a a 1 · · · a n − 1 a a 1 a 1 a 2 · · · a n − 1 a n · · · n−2 ∏