arXiv subjects

Zicong Yang

Publications and source records attributed to Zicong Yang.

6 recordsLinked to original sources

arXiv2026

Weighted Ces\`aro type operators on the weighted Bergman spaces in the unit ball

In this paper, we study weighted Ces\`aro type operators \[ \mathcal C_{\mu,\beta}^{\xi}:A_{\alpha}^{p}(\mathbb B_n) \longrightarrow A_{\alpha}^{q}(\mathbb B_n) \] induced by measures on $[0,1)$, and obtain boundedness characterizations throughout the range $0<p,q\le\infty$. We first extend the corresponding results on the unit disk to the unit ball in the range $1\le p\le q<\infty$. By means of atomic decomposition, we further treat the case $0<p<1$ and $p\le q<\infty$, thereby obtaining a complete characterization for $0<p\le q<\infty$. The latter result is new even in one dimension. For the range $0<q<p\le\infty$, we characterize the boundedness in terms of an integral condition involving the tail function of the inducing measure. This result is also new even on the unit disk. Finally, we characterize the boundedness of the corresponding operators when the target space is $H^\infty(\mathbb B_n)$.

math.FA↗

arXiv2025

Difference of weighted composition operators between some spaces of analytic function spaces

We first obtain a simpler proof of the main results in [IEOT, {\bf 93}(2021), 17], which characterized the bounded and compact differences $C_{u,\varphi}-C_{v,\psi}$ of two weighted composition operators acting between different Bergman spaces. More importantly, we get some characterizations for the difference of two weighted composition operators belonging to Schatten class. Futhermore, the compact difference of two weighted composition operators acting on Hardy-Hilbert spaces is also studied.

math.FA↗

arXiv2025

Essential norm and Schatten class difference of weighted composition operators over the ball

In this paper, we obtain the essential norm estimate for the difference of two weighted composition operators acting on standard weighted Bergman spaces over the unit ball. And we get some characterizations for the difference of weighted composition operators belonging to Schatten class, which has rarely been considered before. Our methods are fundamental, which involve Carleson measures and $R$-Berezin transform.

math.FA↗

arXiv2025

Toeplitz operators and weighted composition operators on variable exponent Bergman spaces

In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson measures. Then they extended the results to the ball setting. In this paper, we further generalize those results to variable exponent Bergman spaces over the unit ball. Our proofs, when restricted to the case of constant variable, are new and simpler. Moreover, boundedness and compactness of Toeplitz operators on variable exponent Bergman spaces are also characterized.

math.FA↗

arXiv2024

A new class of Carleson measures and integral operators on Bergman spaces

Let $n$ be a positive integer and $\mathbf{g}=(g_0,g_1,\cdots,g_{n-1})$, with $g_k\in H(\mathbb{D})$ for $k=0,1,\cdots,n-1$. Let $I_{\mathbf{g}}^{(n)}$ be the generalized Volterra-type operators on $H(\mathbb{C})$, which is represented as $$ I_{\mathbf{g}}^{(n)}f=I^n\left(fg_0+f'g_1+\cdots+f^{(n-1)}g_{n-1}\right), $$ where $I$ denotes the integration operator $$(If)(z)=\int_0^zf(w)dw,$$ and $I^n$ is the $n$th iteration of $I$. This operator is a generalization of the operator that was introduced by Chalmoukis in \cite{Cn}. In this paper, we study the boundedness and compactness of the operator $I_{\mathbf{g}}^{(n)}$ acting on Bergman spaces to another. As a consequence of these characterizations, we obtain conditions for certain linear differential equations to have solutions in Bergman spaces. Moreover, we study the boundedness, compactness and Hilbert-Schmidtness of the following sums of generalized weighted composition operators: Let $\mathbf{u}=(u_0,u_1,\cdots,u_n)$ with $u_k\in H(\mathbb{D})$ for $0\leq k\leq n$ and $φ$ be an analytic self-map of $\mathbb{D}.$ The sums of generalized weighted composition operators is defined by $$L_{\mathbf{u},φ}^{(n)}=\sum_{k=0}^nW_{u_k,φ}^{(k)},$$ where $$W_{u_k,φ}^{(k)}f=u_k\cdot f^{(k)}\circφ.$$ Our approach involves the study of new class of Sobolev-Carleson measures for classical Bergman spaces on unit disk which appears in the first main Theorems \ref{Theorem1.1} and \ref{Theorem1.2}.

math.CV↗

arXiv2024

Generalized Volterra-type integral operators between Bloch-type spaces

The Volterra-type integral operator plays an essential role in modern complex analysis and operator theory. Recently, Chalmoukis \cite{Cn} introduced a generalized integral operator, say $I_{g,a}$, defined by $$I_{g,a}f=I^n(a_0f^{(n-1)}g'+a_1f^{(n-2)}g''+\cdots+a_{n-1}fg^{(n)}),$$ where $g\in H(\mathbb{D})$ and $a=(a_0,a_1,\cdots,a_{n-1})\in \mathbb{C}^n$. $I^n$ is the $n$th iteration of the integral operator $I$. In this paper, we introduce a more generalized integral operators $I_{\mathbf{g}}^{(n)}$ that cover $I_{g,a}$ on the Bloch-type space $\mathcal{B}^α$, defined by $$I_{\mathbf{g}}^{(n)}f=I^n(fg_0+\cdots+f^{(n-1)}g_{n-1}).$$ We show the rigidity of the operator $I_{\mathbf{g}}^{(n)}$ and further the sum $\sum_{i=1}^nI_{g_i}^{N_i,k_i}$, where $I_{g_i}^{N_i,k_i}f=I^{N_i}(f^{(k_i)}g_i)$. Specifically, the boundedness and compactness of $\sum_{i=1}^nI_{g_i}^{N_i,k_i}$ are equal to those of each $I_{g_i}^{N_i,k_i}$. Moreover, the boundedness and compactness of $I^n((fg')^{(n-1)})$ are independent of $n$ when $α>1$.

math.FA↗