Yecheng Shi, Songxiao Li
In this paper, some characterizations for the compact difference of composition operators on Bergman spaces $A^p_ω$ with doubling weight are given, which extend Moorhouse's characterization for the difference of composition operators on the weighted Bergman space $A^2_α$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Schatten-Herz class Toeplitz operators on weighted Bergman spaces induced by doubling weights are investigated in this paper.
The boundedness and compactness of Toeplitz operator from $A_ω^p$ to $A_ω^q$ with doubling weights $ω$ are studied in this paper. The characterizations of Schatten class Toeplitz operators and Volterra operators on $A_ω^2$ are also investigated.
Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_ω$, where $0<p<\infty$ and $ω$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling condition, to a Lebesgue space $L^q_ν$ are characterized. On the way to the proofs a new embedding theorem on weighted Bergman spaces $A^p_ω$ is established. This last-mentioned result generalizes the well-known characterization of the boundedness of the differentiation operator $D^n(f)=f^{(n)}$ from the classical weighted Bergman space $A^p_α$ to the Lebesgue space $L^q_μ$,…
A note on Stević-Sharma type operators between Bergman spaces with doubling weights
本文借助既有文献中的估计，完整刻画了双侧倍权 Bergman 空间之间具有不同权重及复合符号的 Stević-Sharma 型算子的有界性和紧性。
The boundedness of $P_ω:L^\infty(\mathbb{B})\to \mathcal{B}(\mathbb{B})$ and $P_ω(P_ω^+):L^p(\mathbb{B},\upsilon dV)\to L^p(\mathbb{B},\upsilon dV)$ on the unit ball of $\mathbb{C}^n$ with $p>1$ and $ω,\upsilon\in \mathcal{D}$ are investigated in this paper.
Bounded and compact differences of two composition operators acting from the weighted Bergman space $A^p_ω$ to the Lebesgue space $L^q_ν$, where $0<q<p<\infty$ and $ω$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling condition, are characterized. On the way to the proofs a new description of $q$-Carleson measures for $A^p_ω$, with $p>q$ and $ω\in\mathcal{D}$, involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of $q$-Carleson measures for the classical weighted Bergman space $A^p_α$ with $-1…
order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights
本文研究带倍增权Bergman空间上广义加权复合算子的序有界性和本质范数，并利用降阶方法给出本质范数估计。
The boundedness of the small Hankel operator $h_f^ν(g)=P_ν(f\bar{g})$, induced by an analytic symbol $f$ and the Bergman projection $P_ν$ associated to $ν$, acting from the weighted Bergman space $A^p_\om$ to $A^q_ν$ is characterized on the full range $0<p,q<\infty$ when $ω,ν$ belong to the class $\mathcal{D}$ of radial weights admitting certain two-sided doubling conditions. Certain results obtained are equivalent to the boundedness of bilinear Hankel forms, which are in turn used to establish the weak factorization $A_η^{q}=A_ω^{p_{1}}\odot A_ν^{p_{2}}$, where $1<q,p_{1},p_{2}<\infty$ such t…
This paper is devoted to the study of the weighted Bergman space $A_ω^p $ in the unit ball $\mathbb{B}$ of $\mathbb{C}^n$ with doubling weight $ω$ satisfying $$\int_r^1ω(t)dt <C \int_{\frac{1+r}{2}}^1ω(t)dt ,\,\, 0\leq r<1.$$ The $q-$Carleson measures for $A_ω^p$ are characterized in terms of a neat geometric condition involving Carleson block. Some equivalent characterizations for $A_ω^p$ are obtained by using the radial derivative and admissible approach regions. The boundedness and compactness of Volterra integral operator $T_g:A_ω^p\to A_ω^q$ are also investigated in this paper with $0<p\l…
Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights
本文研究椭圆型复合半群在加倍权加权Bergman空间上诱导的复合半群的无穷小生成元的谱，利用谱映射定理和复合算子谱刻画，并探讨最终范数连续性及紧积分算子。
Stević-Sharma type operators between Bergman spaces induced by doubling weights
本文利用 Khinchin 不等式、Geršgorin 定理和原子分解，刻画倍增权加权 Bergman 空间上 Stević-Sharma 型及加权微分复合算子和的范数与本质范数，并获得插值定理。
Toeplitz and Hankel operators on Bergman spaces with doubling weights
本文研究倍权Bergman空间上Toeplitz与Hankel算子的有界性和紧性，通过Berezin变换刻画有界性，并给出共解析符号情形下的充要条件。
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted Bergman-Orlicz spaces, different from $H^{\infinity}$, on which every composition operator is bounded.
A radial weight $ω$ belongs to the class $\widehat{\mathcal{D}}$ if there exists $C=C(ω)\ge 1$ such that $\int_r^1 ω(s)\,ds\le C\int_{\frac{1+r}{2}}^1ω(s)\,ds$ for all $0\le r<1$. Write $ω\in\check{\mathcal{D}}$ if there exist constants $K=K(ω)>1$ and $C=C(ω)>1$ such that $\widehatω(r)\ge C\widehatω\left(1-\frac{1-r}{K}\right)$ for all $0\le r<1$. In a recent paper, we have recently prove that these classes of radial weights arise naturally in the operator theory of Bergman spaces induced by radial weights. Classical results by Hardy and Littlewood, and Shields and Williams, show that the weig…
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_α^2$ with respect to some conjugations. Then we provide some examples of these operators.
In this paper, the boundedness and compactness of the difference of composition-differentiation operators $D_φ-D_ψ$ acting from Hardy spaces $H^p$ to weighted Bergman spaces $A^q_α$ are completely characterize for all $0<p,q<\infty$.
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space.
Compact differences of two weighted composition operators acting from the weighted Bergman space $A^p_ω$ to another weighted Bergman space $A^q_ν$, where $0<p\le q<\infty$ and $ω,ν$ belong to the class $\mathcal{D}$ of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of $q$-Carleson measures for $A^p_ω$, with $ω\in\mathcal{D}$, in terms of pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of $q$-Carleson measures for the classical weighted Bergman space $A^p_α$ with …
In this paper, we study the complex symmetry of weighted composition-differentiation operator $D_{n, ψ, ϕ}$ on weighted Bergman spaces $\mathcal{A}^2_α$ with respect to the conjugation $C_{μ, η}$ for $μ, η\in \{z\in \mathbb{C}:|z|=1\}$. We obtain explicit conditions for which the operator $D_{n, ψ, ϕ}$ is Hermitian and normal. We also characterize the complex symmetric weighted composition-differentiation operator for derivative Hardy spaces.
We obtain some estimates for norm and essential norm of the difference of two composition operators between weighted Bergman spaces $A^p_α$ and $A^q_β$ on the unit ball. In particular, we completely characterize the boundedness and compactness of $C_φ-C_ψ: A^p_α\to A^q_β$ for full range $0<p,q<\infty$, $-1<α,β<\infty$.
In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_φ$ on Bergman type spaces $A_ω^p $ with double weight $ω$. Let $X=\{u\in H(D): uC_φ:A_ω^p\to A_ω^p \mbox{ is bounded}\}.$ For some regular weights $ω$, we obtain that $X=H^\infty$ if and only if $φ$ is a finite Blaschke product.
Let $\mathcal{D}$ be the class of radial weights on the unit disk which satisfy both forward and reverse doubling conditions. Let $g$ be an analytic function on the unit disk $\mathbb{D}$. We characterize bounded and compact Volterra type integration operators \[ J_{g}(f)(z)=\int_{0}^{z}f(λ)g'(λ)dλ\] between weighted Bergman spaces $L_{a}^{p}(ω)$ induced by $\mathcal{D}$ weights and Hardy spaces $H^{q}$ for $0<p,q<\infty$.
In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of conjugations. As it turns out, weighted composition operators enhanced by a symmetry must be bounded. Hermitian, and unitary weighted composition operators are proven to be complex symmetric with respect to an adapted and highly relevant conjugation. We classify which the linear fractional functions give rise to the complex symmetry of bounded composition operators. We …
We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit disk. A generalized Toeplitz operator is defined and the boundedness, compactness and Schatten class of this operator are investigated on the Hilbert weighted Bergman space. As an application, Schatten class membership of generalized Volterra integral operators are also characterized. Finally, we also get the characterizations of Schatten class membership of generalized Toeplitz operator and generalized Volterra integral operators on the Hardy spac…
On the Berezin range of Toeplitz and weighted composition operators on weighted Bergman spaces
本文刻画了加权Bergman空间上调和符号Toeplitz算子的Berezin值域，引入一类新的加权复合算子并确定其Berezin值域与Berezin数，同时研究了复合算子Berezin值域的凸性及原点与闭包的关系。
Toeplitz operators and weighted composition operators on variable exponent Bergman spaces
本文将Choe等人关于加权复合算子之差有界性与紧性的Carleson测度刻画推广到单位球上的变指数Bergman空间，并给出更简单的新证明，同时刻画了Toeplitz算子的有界性与紧性。
This paper is based on the course \lq\lq Weighted Hardy-Bergman spaces\rq\rq\, I delivered in the Summer School \lq\lq Complex and Harmonic Analysis and Related Topics\rq\rq at the Mekrijärvi research station of University of Eastern Finland, June $2014$. The main purpose of this survey is to present recent progress on the theory of Bergman spaces $A^p_ω$, induced by radial weights $ω$ satisfying the doubling property $\int_r^1ω(s)\,ds\le C\int_{\frac{1+r}{2}}^1ω(s)\,ds$.
We use induction and interpolation techniques to prove that a composition operator induced by a map $ϕ$ is bounded on the weighted Bergman space $\A^2_α(\mathbb{H})$ of the right half-plane if and only if $ϕ$ fixes $\infty$ non-tangentially, and has a finite angular derivative $λ$ there. We further prove that in this case the norm, essential norm, and spectral radius of the operator are all equal, and given by $λ^{(2+α)/2}$.
We characterize the Schatten class Toeplitz operators induced by a positive Borel measure on the unit disc and the reproducing kernel of the Bergman space $A^2_ω$, where $ω$ is a radial weight satisfying the doubling property $\int_r^1ω(s)\,ds\le C\int_{\frac{1+r}{2}}^1ω(s)\,ds$. By using this, we describe the Schatten class composition operators. We also discuss basic properties of composition operators acting from $A^p_ω$ to $A^q_v$.
Cyclic phenomena for composition operators on weighted Bergman spaces
本文完全刻画了右半平面加权Bergman空间上由仿射自映射诱导的循环和超循环复合算子，从而完成了所有超循环、超循环和循环复合算子的分类。
Let $A^p_ω$ denote the Bergman space in the unit disc induced by a radial weight~$ω$ with the doubling property $\int_{r}^1ω(s)\,ds\le C\int_{\frac{1+r}{2}}^1ω(s)\,ds$. The positive Borel measures such that the differentiation operator of order $n\in\mathbb{N}\cup\{0\}$ is bounded from $A^p_ω$ into $L^q(μ)$ are characterized in terms of geometric conditions when $0<p,q<\infty$. En route to the proof a theory of tent spaces for weighted Bergman spaces is built.
Optimal off-diagonal upper estimates for Bergman reproducing kernels
研究单位圆盘上伯格曼再生核的非对角线上界估计，基于权重矩的单边加倍条件证明其精确性及刻画性。通过新方法得到修正伯格曼核的\(L^p\)均值估计，建立相关函数与测度新联系，还将结果推广到高维等情况。
In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_α^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit ball of the $N$-dimensional complex space. By taking $N=1$, $\mathbb{B}_N=\mathbb{D}$ the unit disc, we also complete the discussion about the spectrum of a weighted composition operator when it is invertible on $H^2(\mathbb{D})$ or $A_α^2(\mathbb{D})$.
The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calderón-Zygmund operators in harmonic analysis. Using this tool from harmonic analysis, some new characterizations are given for the boundedness and compactness of weighted composition operators acting between weighted Bergman spaces in the upper half plane. Moreover, we establish a new weighted type estimate for the holomorphic Bergman-class functions, for a new class of weights, which is adapted to Sa…
Difference of weighted composition operators on weighted Bergman spaces over the unit Ball
本文在单位球上刻画了加权Bergman空间到Lebesgue空间的加权复合算子差的有界性与紧致性，推广了单位圆盘结果，并给出了q-Carleson测度的新刻画。
We show that the weighted Bergman-Orlicz space $A\_α^ψ$ coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function $ψ$ satisfies the so-called $Δ^{2}$--condition. In addition we prove that this condition characterizes those $A\_α^ψ$ on which every composition operator is bounded or order bounded into the Orlicz space $L\_α^ψ$. This provides us with estimates of the norm and the essential norm of composition operators on such spaces. We also prove that when $ψ$ satisfies the $Δ^{2}$--condition, a composition operator is compact on $A\_α^ψ$ if and only …
Recently the authors characterized the Fredholmn properties of Toeplitz operators on weighted Fock spaces when the Laplacian of the weight function is bounded below and above. In the present work the authors extend their characterization to doubling Fock spaces with a subharmonic weight whose Laplacian is a doubling measure. The geometry induced by the Bergman metric for doubling Fock spaces is much more complicated than that of the Euclidean metric used in all the previous cases to study Fredholmness, which leads to considerably more involved calculations.
Compactness of composition operators on the Bergman space of the bidisc
本文研究双圆盘Bergman空间上复合算子的紧性，证明了在闭包上Lipschitz连续的全纯自映射φ所诱导的复合算子C_φ为紧算子的充分必要条件，用两个边界交集为空的条件刻画了紧性。
The zero sets of the Bergman space $A^p_ω$ induced by either a radial weight $ω$ admitting a certain doubling property or a non-radial Bekollé-Bonami type weight are characterized in the spirit of Luecking's results from 1996. Accurate results obtained en route to this characterization are used to generalize Horowitz's factorization result from 1977 for functions in $A^p_ω$. The utility of the obtained factorization is illustrated by applications to integration and composition operators as well as to small Hankel operator induced by a conjugate analytic symbol. Dominating sets and sampling mea…
Embedding theorems for Bergman-Zygmund spaces induced by doubling weights
本文研究了由双倍权重诱导的Bergman-Zygmund空间中恒等映射和微分算子的有界性和紧性条件。
In thius paper we introduce the Hardy and Bergman spaces on hyperconvex domains relative to a acontinuous exhaustion function. We prove their basic properties and study their composition operators induced by holomorphic mappings between domains.
We study the compactness of composition operators on the Bergman spaces of certain bounded pseudoconvex domains in $\mathbb{C}^n$ with non-trivial analytic disks contained in the boundary. As a consequence we characterize that compactness of the composition operator with a holomorphic, continuous symbol (up to the closure) on the Bergman space of the polydisk.
Suppose that $ω$ is a radial weight on the unit disk that satisfies both forward and reverse doubling conditions. Using Carleson measures and $T1$-type conditions, we obtain necessary and sufficient conditions of the positive Borel measure $μ$ such that the Toeplitz operator $T_{μ,ω}:L^p_a(ω)\to L_a^1(ω)$ is bounded and compact for $0<p\leq 1$. In addition, we obtain a bump condition for the bounded Toeplitz operators with $L^1(ω)$ symbol on $L^1_a(ω)$. This generalizes a result of Zhu in \cite{zhu1989}.
We study the boundedness of composition operators on the weighted Bergman spaces and the Hardy space over the polydisc. For arbitrary polydisc we prove the rank sufficiency theorem which, in particular, provides us with a simple criterion describing boundedness of composition operators on the spaces over the bidisc. Such a consistent characterization is obtained for the classical Bergman space over the tridisc.
Composition and Volterra type operators on large Bergman spaces with rapidly decreasing weights
本文刻画了快速递减权大 Bergman 空间之间广义 Volterra 型积分算子的有界性、紧性与 Schatten 类性质，利用 Littlewood-Paley 公式和嵌入定理推广了 Pau 与 Peláez 的积分算子研究。
We study the compactness of composition operators on the Bergman spaces of certain bounded convex domains in $\mathbb{C}^n$ with non-trivial analytic discs contained in the boundary. As a consequence we characterize that compactness of the composition operator with a continuous symbol (up to the closure) on the Bergman space of the polydisc.
Sums of two generalized weighted composition operators between Bergman spaces
本文研究Bergman空间上两个不同符号和阶数的广义加权复合算子之和，通过伪双曲圆盘原像的划分，证明其有界性与紧性由各和项单独决定。
We consider Volterra-type integration operators $T_g$ between Bergman spaces induced by weights $ω$ satisfying a doubling property. We derive estimates for the operator norms, essential and weak essential norms of $T_g: A_ω^p \to A_ω^q$, $0<p\leq q<\infty$. In particular, the operator $T_g: A_ω^1\to A_ω^1$ is weakly compact if and only if it is compact.
We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2ϕ})$ where $ϕ$ is a subharmonic function with $Δϕ$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $Δϕ$.
Let $ϕ$ be an analytic self-map and $u$ be a fixed analytic function on the open unit disk $D$ in the complex plane $\CC.$ The weighted composition operator is defined\break by \begin{equation*} uC_ϕf =u \cdot (f\circ ϕ), f \in H(D). \end{equation*} Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function theoretic properties of their inducing maps.
Let $Ω\subset \mathbb{C}^n$ be a smooth bounded pseudoconvex domain and $A^2 (Ω)$ denote its Bergman space. Let $P:L^2(Ω)\longrightarrow A^2(Ω)$ be the Bergman projection. For a measurable $φ:Ω\longrightarrow Ω$, the projected composition operator is defined by $(K_φf)(z) = P(f \circ φ)(z), z \inΩ, f\in A^2 (Ω).$ In 1994, Rochberg studied boundedness of $K_φ$ on the Hardy space of the unit disk and obtained different necessary or sufficient conditions for boundedness of $K_φ$. In this paper we are interested in projected composition operators on Bergman spaces on pseudoconvex domains. We study…
We study big Hankel operators $H_f^ν:A^p_ω\to L^q_ν$ generated by radial Bekollé-Bonami weights $ν$, when $1<p\leq q<\infty$. Here the radial weight $ω$ is assumed to satisfy a two-sided doubling condition, and $A^p_ω$ denotes the corresponding weighted Bergman space. A characterization for simultaneous boundedness of $H_f^ν$ and $H_{\overline{f}}^ν$ is provided in terms of a general weighted mean oscillation. Compared to the case of standard weights that was recently obtained by Pau, Zhao and Zhu (Indiana Univ. Math. J. 2016), the respective spaces depend on the weights $ω$ and $ν$ in an esse…
In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators are not assumed to be bounded. The properties of weighted composition operators such as real symmetry, unitariness, complex symmetry, are characterized fully in simple algebraic terms, involving their symbols. As it turns out, a weighted composition operator having a symmetric structure must be bounded. We also obtain the interesting consequence that real sym…
Let $Ω\subset \mathbb{C}^n$ for $n\geq 2$ be a bounded pseudoconvex domain with a $C^2$-smooth boundary. We study the compactness of composition operators on the Bergman spaces of smoothly bounded convex domains. We give a partial characterization of compactness of the composition operator (with sufficient regularity of the symbol) in terms of the behavior of the Jacobian on the boundary. We then construct a counterexample to show the converse of the theorem is false.
Cesàro operator induced by a Bergman kernel
本文研究由加权Bergman空间再生核诱导的Cesàro型算子在Hardy空间和加权Bergman空间上的有界性，利用尾积分或矩给出完全刻画，结果在标准权及Cauchy核情形下亦为新。
Composition operators on function spaces on the halfplane: spectra and semigroups
本文研究了右半平面 Zen 空间上的复合算子，推广了关于范数、本质范数、（本质）谱及半群的已有工作，并通过 Hardy--Bergman 空间实例说明结果。
We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators generated by polynomial symbols $φ$ on a scale of Bergman--type Hilbert spaces $\mathcal{D}_α$. We investigate the optimal $β$ such that the composition operator $\mathcal{C}_φ$ maps $\mathcal{D}_α$ boundedly into $\mathcal{D}_β$. We also prove a new embedding theorem for the non-Hilbertian Hardy space $\mathcal H^p$ into a Bergman space in the half-plane and …
We characterize strong continuity of general operator semigroups on some Lebesgue spaces. In particular, a characterization of strong continuity of weighted composition semigroups on classical Hardy spaces and weighted Bergman spaces with regular weights is given. As applications, our result improves the results of Siskakis, A. G. \cite{AG1} and König, W. \cite{K} and answers a question of Siskakis, A. G. proposed in \cite{AG4}. We also characterize strongly continuous semigroups of weighted composition operators on weighted Bergman spaces in terms of abelian intertwiners of multiplication ope…
Let $A^p_ω$ denote the Bergman space in the unit disc $\mathbb{D}$ of the complex plane induced by a radial weight $ω$ with the doubling property $\int_{r}^1ω(s)\,ds\le C\int_{\frac{1+r}{2}}^1ω(s)\,ds$. The tent space $T^q_s(ν,ω)$ consists of functions such that \begin{equation*} \begin{split} \|f\|_{T^q_s(ν,ω)}^q =\int_{\mathbb{D}}\left(\int_{Γ(ζ)}|f(z)|^s\,dν(z)\right)^\frac{q}sω(ζ)\,dA(ζ) <\infty,\quad 0<q,s<\infty. \end{split} \end{equation*} Here $Γ(ζ)$ is a non-tangential approach region with vertex $ζ$ in the punctured unit disc $\mathbb{D}\setminus\{0\}$. We characterize the positive B…
Composition Operators and Rational Inner Functions II: Boundedness between two different Bergman Spaces
本文研究非光滑有理内函数诱导的复合算子在两个不同Bergman空间间的有界性，给出了对应参数条件下的一个充分条件。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。