Difference of weighted composition operators on weighted-type spaces in the unit ball
Bingyang Hu, Songxiao Li
本文给出了$\mathbb{C}^n$的单位球上的加权型空间上两个加权复合算子差的有界性、紧性和本质范数的一个新的刻画.
In this paper, a new characterization is provided for the boundedness, compactness and essential norm of the difference of two weighted composition operators on weighted-type spaces in the unit ball of $\mathbb{C}^n$.
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
Weak factorization and Hankel forms for weighted Bergman spaces on the unit ball
建立了加权Bergman空间$A^p_{\a}$的弱分解，其中$1<p<\infty$为$\C^n$的单位球上的两个加权Bergman空间.为了得到这个结果，我们刻画了$\C^n$的单位球上的加权Bergman空间上的有界Hankel型.
Weighted Composition Operators from $H^\infty$ to the Bloch Space in the Unit Ball of Cn
研究了Cn中单位球上从$H^\infty$到Bloch空间的加权复合算子的有界性和紧性.特别地，给出了加权复合算子的有界性和本质范数的一些新的刻画。
Composition operators on Bergman-Orlicz spaces on the ball
我们给出了球上加权Bergman-Orlicz空间的嵌入定理，然后将我们的结果应用于这种背景下复合算子的研究。作为本文的动机之一，我们证明了存在不同于$H^{\infinity}$的加权Bergman-Orlicz空间，在该空间上每个复合算子都是有界的.
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。
Spectra of some invertible weighted composition operators on Hardy and weighted Bergman spaces in the unit ball
本文研究了带自同构符号的可逆加权复合算子在Hardy空间$H^2(\mathbb{B}_N)$和加权Bergman空间$A_α^2(\mathbb{B}_N)$上的谱，其中$\mathbb{B}_N$是$N$维复空间的单位球.以$N=1$，$\mathbb{B}_N=\mathbb{D}$为单位圆，完成了加权复合算子在$H^2(\mathbb{D})$或$A_α^2(\mathbb{D})$上可逆时的谱的讨论.
Carleson Measures and Toeplitz operators for weighted Bergman spaces on the unit ball
给出了单位球上涉及函数乘积的加权Bergman空间的Carleson测度的一些新的刻画。对于这些，我们刻画加权Bergman空间之间的有界和紧Toeplitz算子。上述结果被应用于刻画有界紧扩张Cesàro算子和点态乘法算子.结果是新的，即使在单位磁盘的情况下。
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 $0<p,q<\infty$, $-1<α,β<\infty$.
Compact Differences of Composition Operators on Holomorphic Function Spaces in the Unit Ball
我们找到了作用于$H^2(B_N)$或$A^2_s(B_N)$（$s>-1$）上的两个复合算子之差的本质范数的一个下界.这一结果在证明线性分式复合算子的差是紧的一个充要条件方面起到了重要作用，回答了MacCluer和Weir在2005年提出的一个问题。
Norm Equivalence and Composition Operators on Bloch/Lipschitz spaces of the Unit Ball
当0<p<1时，n维复欧氏空间中单位球的p-Bloch空间和（1-p）-Lipschitz空间作为集合是相等的。我们证明了这些空间是额外的范数等价的，从而扩展了已知的结果n=1和polydisk。作为应用，我们通过研究球上p-和q-Lipschitz空间之间的复合算子的有界性，推广了Madigan在圆盘上的工作.
Essential norm and Schatten class difference of weighted composition operators over the ball
研究单位球上加权 Bergman 空间中两个加权复合算子之差，利用 Carleson 测度和 $R$-Berezin 变换估计其本性范数，并刻画其属于 Schatten 类的条件。
Weighted composition operators on Hilbert function spaces on the ball
本文研究了在球上Hilbert函数空间上的带权复合算子，揭示了不同空间下算子的单位ary性质差异，扩展了圆盘上的相关结论。
Hadamard gap series in weighted-type spaces on the unit ball
本文给出了Hadamard间隙$\CC^n$中单位球$\BB$上解析函数$f(z)$的一个充要条件，即在对权函数$μ$所设的一定条件下，$f(z)=\sum_{k=1}^\infty P_{n_k}(z)$属于加权型空间$H^\infty_μ$和相应的小加权型空间$H^\infty_{μ, 0}$，其中$P_{n_k}(z)$是$n_k$和$n_{k+1}/n_k \ge c>1$的次齐次多项式.我们还研究了这些函数在$H^\infty_μ$中的增长率。最后，我们刻画了从加权型空间$H^\infty_μ$到混合范数空间的加权复合算子的有界性和紧性。
In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study weighted composition operators between them in detail. In particular, we characterize bounded and compact weighted composition operators between discrete Hardy spaces. We also consider isometric weighted composition operators between these spaces.
Weighted Composition Operators from $F(p,q,s)$ to Bloch Type Spaces on the Unit Ball
设$ϕ(z)=(ϕ_1(z),...,ϕ_n(z))$是$B$的全纯自映射，$ψ(z)$是$B$上的全纯函数，其中$B$是${\Bbbb C}^n$的单位球.设$0<p,s<+\infty, -n-1<q<+\infty, q+s>-1$和$α\geq 0,$，本文给出了由$ϕ$和$ψ$诱导的加权复合算子$\wco$在空间$\Fs$和$α$ -{ \sl Bloch}空间$β^α.$之间有界紧的充要条件
In this paper, we completely characterize the order boundedness of weighted composition operators between different weighted Dirichlet spaces and different derivative Hardy spaces.
Quasinormal and hyponormal weighted composition operators on $H^2$ and $A^2_α$ with linear fractional compositional symbol
本文研究了Hardy空间和加权Bergman空间上的拟正规和亚正规复合算子\W，其复合符号为线性分式$\ph$.我们刻画了由这些映射和许多这样的加权复合算子在$H^{2}$和$A_α^{2}$上诱导的拟正规复合算子，表明它们在所有已知情况下必然正规.我们消除了几种可能的亚正规加权复合算子，但也给出了新的例子，亚正规加权复合算子的$H^2$这不是拟正规的。
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 work, we extend the theory of Békollè-Bonami $B_p$ weights. Here we replace the constant $p$ by a non-negative measurable function $p(\cdot),$ which is log-Hölder continuous function with lower bound $1$. We show that the Bergman projector on the unit ball of $\mathbb C^n$ is continuous on the weighted variable Lebesgue spaces $L^{p(\cdot)}(w)$ if and only if $w$ belongs to the generalised Békollè-Bonami class $B_{p(\cdot)}$. To achieve this, we define a maximal function and show that it is bounded on $L^{p(\cdot)}(w)$ if $w\in B_{p(\cdot)}$. We next state and prove a weighted extrapol…
In this paper, we consider \emph{unbounded} weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as $\calC$-selfadjoint (with respect to weighted composition conjugations), Hermitian, normal, cohyponormal, and invertible. In addition, the paper shows that unbounded normal weighted composition operators are contained properly in the class of $\calC$-selfadjoint operators with respect to weighted composition conjugations. The computation of the spectrum is carried out in detail.
Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space
本文给出了从加权Bergman空间和Hardy空间到Bloch空间的加权复合算子的本质范数的估计和有界性与紧性的一个新的刻画.
Essential Norms of Weighted Composition Operators between Hardy Spaces in the unit Ball
设$ϕ(z)=(ϕ_1(z),...,ϕ_n(z))$是$B_n$的全纯自映射，$ψ(z)$是$B_n$上的全纯函数，$H(B_n)$是$B_n$上的全纯函数类，其中$B_n$是$C^n$的单位球，权合成算子$W_{ψ,ϕ}$由$W_{ψ,ϕ}=ψf(ϕ)$定义，其中$f\in H(B_n)$是$f\in H(B_n)$的权合成算子.本文估计了从Hardy空间$H^p$到$H^q$（$0<p,q\leq \infty$）的加权复合算子$W_{ψ,ϕ}$的本质范数.当$p=\infty$和$q=2$时，给出了本质范数的精确公式.作为它们的应用，我们还得到了从$H^p$到$H^q$的有界加权复合算子是紧的一些充要条件。
Differences of weighted differentiation composition operators from Bloch-type space to weighted-type space
本文给出了从Bloch型空间到加权型空间的加权微分复合算子差的有界性和紧性的几个新的等价刻画。特别地，我们用单位圆盘上导出的解析自映射的$n$次方估计了它的本质范数。
Norm and essential norm of a weighted composition operator on the Bloch space
给出了Bloch空间上加权复合算子的范数和本质范数的一些新的估计。作为推论，我们得到了Bloch空间上加权复合算子的有界性和紧性的一些新的刻画。
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 …
Differences of Weighted Composition Operators from $H^\infty$ to the Bloch Space
本文给出了从$H^\infty$到Bloch空间的两个加权复合算子差的有界性和紧性的两个新的刻画.
In this paper, we investigate the complex symmetric structure of generalized weighted composition operators $D_{m,ψ,φ}$ on the weighted Hardy space $H^2(β)$. We obtain explicit conditions for $ D_{m,ψ,φ}$ to be complex symmetric with the conjugation $J_w$. Under the assumption that $ D_{m,ψ,φ}$ is $J_w$-symmetric, some sufficient and necessary conditions for $D_{m,ψ,φ}$ to be Hermitian and normal are given.
We study the cyclic and supercyclic dynamical properties of weighted composition operators on the Fock space $\mathcal{F}_2$. A complete characterization of cyclicity which depends on the derivative of the symbol for the composition operator and zeros of the weight function is provided. It is further shown that the space fails to support supercyclic weighted composition operators. As a consequence, we also noticed that the space supports no cyclic multiplication operator.
Volterra type and weighted composition operators on Fock spaces
讨论了作用在加权Fock空间上的Volterra型积分算子和复合算子的有界紧积。我们还估计了这些运营商的Berezin型积分变换复计划$\mathbb{C}$的范数。我们的所有结果是有效的加权复合算子的一类Fock空间考虑适当的解释下的重量。
This paper characterises the boundedness and compactness of Agler--McCarthy monomial operators by reducing them to weighted composition operators and deriving explicit Carleson measure criteria on the half-plane. The results are illustrated by examples.
Which weighted composition operators are complex symmetric?
最近几位作者的工作揭示了许多意想不到的正常加权复合算子类的存在。另一方面，已知每个正规算子都是复对称算子。因此，我们进行研究复杂的对称加权复合算子，确定几个新的类这样的运营商。
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.
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.
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。
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…
Rigidity of weighted composition operators on $H^p$
我们证明了每个非紧加权复合算子$f \mapsto u\cdot (f\circϕ)$作用在Hardy空间$H^p$上，为$1 \leq p < \infty$固定了数列空间$\ell^p$的同构拷贝，因此不是严格奇异的。我们还刻画了$H^p$上固定希尔伯特空间$\ell^2$副本的加权复合算子。这些结果推广了以前的非加权复合算子。
Carleson-Type Measures and Kernel Estimates for Potential-Harmonic Weighted Bergman Spaces on the Unit Ball
本文研究了C^n单位球上的加权Bergman空间，建立了Carleson嵌入的刻画，并证明了再生核函数的逐点和范数估计。
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 $0<p,q<\infty$.
For pairs of holomorphic maps $(u,ψ)$ on the complex plane, we study some dynamical properties of the weighted composition operator $W_{(u,ψ)}$ on the Fock spaces. We prove that no weighted composition operator on the Fock spaces is supercyclic. Conditions under which the operators satisfy the Ritt's resolvent growth condition are also identified. In particular, we show that a non-trivial composition operator on the Fock spaces satisfies such a growth condition if and only if it is compact.
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…
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…
Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex symmetry, real symmetry, or isometry are characterized in simple algebraic terms, involving their symbols.
Quantum matrix ball: the weighted Bergman kernels
我们继续研究在q-alg/9703005中引入的Cartan域的q-类似物，并转向复矩阵空间中的球的情况。正的$U_q\frak{su}_{nm}$ -不变积分的显式表达式（见math.QA/9803110）用于定义加权Bergman空间的q-类似物。这些空间上的正交投影是积分算子，本文给出了它们的核的显式公式。
Difference of weighted composition operators between some spaces of analytic function spaces
本文简化了不同Bergman空间间加权复合算子差有界与紧性的证明，刻画了Schatten类中两个加权复合算子差的特征，并研究了Hardy-Hilbert空间上加权复合算子差的紧性。
In this paper, we present the current results in the study of weighted composition operators on the Bloch space of bounded homogeneous domains in $\mathbb{C}^n$ with particular emphasis on the issues of boundedness and compactness. We also discuss the bounded and the compact weighted composition operators from the Bloch space to the Hardy space $H^\infty$.
We consider inductive limits of weighted spaces of holomorphic functions in the unit ball of $\mathbb C^n$. The relationship between sets of uniqueness, weakly sufficient sets and sampling sets in these spaces is studied. In particular, the equivalence of these sets, under general conditions of the weights, is obtained.
We study, to certain Banach spaces $X$, families of weighted composition operators. Notably, we show that if this family form a strongly continuous semigroup, then its infinitesimal generator ($Γ, D(Γ)$) is given by $Γf = gf+Gf^\prime$ with $D(Γ) = \{ f\in X \ | \ gf+Gf^\prime\in X \}$ where $g, G$ are holomorphic functions. Moreover, our second maim result is to study the reciprocal implication. That is if $(Γ, D(Γ))$, define like above, generate a strongly continuous semigroup, then this one is a family of weighted composition operators.
We prove that the weighted composition operator $W_{ϕ,φ}$ fixes an isomorphic copy of $\ell^p$ if the operator $W_{ϕ,φ}$ is not compact on the derivative Hardy space $S^p$. In particular, this implies that the strict singularity of the operator $W_{ϕ,φ}$ coincides with the compactness of it on $S^p$. Moreover, when $p\neq2$, we characterize the conditions for those weighted composition operators $W_{ϕ,φ}$ on $S^p$ which fix an isomorphic copy of $\ell^2$ .
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol inducing the composition operator is an affine function, we give criteria for boundedness and compactness. We also study the cyclicity property and as a byproduct give a sufficient condition so that the direct sum of the identity plus a weighted forward shift operator on the Hardy space H^2 is cyclic.
Convexity of the Berezin range of composition operators induced by automorphisms of the Unit Ball in $\mathbb{C}^n$
本文研究单位圆盘和单位球自同构诱导的复合算子的 Berezin 值域凸性，给出了与酉映射复合的线性分式自同构情形下凸性的新刻画。
Closures of Harmonic Bergman Besov Spaces in the Weighted Harmonic Bloch Spaces on the Unit Ball
本文通过可逆径向微分算子，利用自然水平集刻画了Rn单位球上加权调和Bloch空间中调和Bergman Besov空间的闭包，并首先证明了该空间包含于加权调和小Bloch空间。
Weighted norm inequalities of various square functions and Volterra integral operators on the unit ball
本文研究复单位球上的平方函数与Volterra积分算子，证明了泊松积分相关Lusin面积积分的A_p权加权不等式（解答公开问题），得到全纯函数加权Hardy空间的等价刻画及Volterra算子的加权不等式。
Operators commuting with complex symmetric weighted composition operators on $H^2$
本文研究 Hardy 空间上加权复合算子与复对称加权复合算子的交换性，给出符号条件，并依据符号不动点证明其正规性与复对称性。
A Weighted Estimate for the Square Function on the Unit Ball in $\C^n$
本文证明了在加权空间$L^2(w)$中，$\C^n$的单位球上的Lusin面积积分或平方函数，根据权的不变量$A_2$特征，有一个线性界.我们展示了与平方函数的加权$L^2(w)$范数相关的“面积积分”的无量纲估计。我们证明了经典的和不变的$A_2$类的等价性。
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…
Weighted composition operators between different Fock spaces
研究了作用于Fock空间之间的加权复合算子。得到了以下结果：（1）复合算子空间的有界性和紧性的判别准则;（2）紧差和本质范数的刻画;（3）复合算子空间和非零加权复合算子空间的路连通分支和孤立点的完全刻画.
Weighted composition operators between Fock spaces in several variables
我们得到了$\mathbb{C}^n$中不同Fock空间之间加权复合算子的有界性和紧性的判别准则。我们也给出了这些算子的本质范数的估计。
In this paper, we study the boundedness and compactness of the differences of two weighted composition operators acting from $α$-Bloch space to $β$-Bloch space on the open unit disk. This study has a relationship to the topological structure of weighted composition from $α$-Bloch space to $β$-Bloch space.
Weighted Bergman kernel, directional Lelong number and John-Nirenberg exponent
设$ψ$是闭单位球上的多重次调和函数，$K_{tψ}(z)$是单位球上关于权值$tψ$的Bergman核。我们证明了$K_{tψ}(z)$的边界表现是由$ψ$的某个方向Lelong数决定的，对于所有的$t$，小于与某个非各向同性球族相关联的$ψ$的John-Nirenberg指数，它总是为正的。
Product of Volterra type integral and composition operators on weighted Fock spaces
我们刻画了作用于加权Fock空间之间的Volterra型积分算子和复合算子的有界、紧和Schatten类乘积。我们的结果表示为复平面$\CC$上的某些Berezin型积分变换。我们还利用积分变换估计了这些算子的范数和本质范数。我们的所有结果是有效的加权复合算子之间的一类加权Fock空间考虑。
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。
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。