Composition followed by differentiation from H∞ and the Bloch space to nth weighted-type spaces on the unit disk

Integral-type operators acting between weighted-type spaces on the unit ball

On some product-type operators from Hardy–Orlicz and Bergman–Orlicz spaces to weighted-type spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

/pdf/on-an-integral-type-operator-from-zygmund-type-spaces-to-3gveqx8dh2.pdf

On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

Let $${\varphi}$$
 be an analytic self-map of the unit disk $${\mathbb{D}}$$
 , $${H(\mathbb{D})}$$
 the space of analytic functions on $${\mathbb{D}}$$
 and $${g \in H(\mathbb{D})}$$
 . The boundedness and compactness of the operator $${DC_\varphi : H^\infty \rightarrow { \mathcal Z}}$$
 are investigated in this paper.

Composition Followed by Differentiation Between H ∞ and Zygmund Spaces

Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball

Let ϕ be an analytic self-map of the unit disk &#x1d53b;, H(&#x1d53b;) the space of analytic functions on &#x1d53b; and u ∈ H(&#x1d53b;). 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 Mixed-Norm to Zygmund Spaces

Let $H(\mathbb{D})$ denote the space of all analytic functions on the unit disc $\mathbb{D}$ of the complex plane ℂ, $\psi_{1},\psi_{2}\in H(\mathbb{D}) $, and φ be an analytic self-map of $\mathbb{D}$. In this paper, we characterize the boundedness and compactness of a Stevic-Sharma operator $T _{\psi_{1},\psi_{2},\varphi}$ from Hardy spaces $H^{p}$ (with $1\leq p<\infty$) to the logarithmic Bloch spaces $\mathcal{B}_{\mathrm{log}}$.

https://link.springer.com/content/pdf/10.1186%2Fs13660-015-0547-1.pdf

On a Stević-Sharma operator from Hardy spaces to the logarithmic Bloch spaces

Let $H({\mathbb {B}})$ denote the space of all holomorphic functions on the unit ball ${\mathbb {B}}$ of $ {\mathbb {C}}^n$, $\psi _1,\psi _2,\psi _3\in H({\mathbb {B}}) $ and $\varphi $ be a holomorphic self-map of $ {\mathbb {B}}$. This paper studies the boundedness and compactness of the following extension of the Stevic–Sharma operator, recently proposed by Liu and Yu 

$$\begin{aligned} T_{\psi _1, \psi _2, \psi _3,\varphi }f(z)=\psi _1(z)f(\varphi (z))+\psi _2(z){{\mathcal {R}}}f(\varphi (z))+\psi _3(z){{\mathcal {R}}}\left( f\circ \varphi \right) (z), z\in {\mathbb {B}}, \end{aligned}$$

where ${{\mathcal {R}}}f(z)$ is the radial derivative of $f$ at $z$, from the general space $F(p, q, s)$ to the weighted-type space $H_{\mu }^\infty $ or the little weighted-type space $H_{\mu ,0}^\infty $ on the unit ball.

Yanyan Yu

Papers

Composition Followed by Differentiation Between H ∞ and Zygmund Spaces

Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball

Weighted Differentiation Composition Operators from Mixed-Norm to Zygmund Spaces

On a Stević-Sharma operator from Hardy spaces to the logarithmic Bloch spaces

On an Extension of Stević–Sharma Operator from the General Space to Weighted-Type Spaces on the Unit Ball