Haichou Li, Jinsong Liu, Hongyu Wang
Following M.Abate and A.Saracco's work on strongly pseudoconvex domains in $\mathbb{C}^n$, we characterize Carleson measures of $A^2(D)$ in bounded convex domains with smooth boundary of finite type. We also give examples of Carleson measures with uniformly discrete (with respect to the Kobayashi distance) sequences.
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A note for Carleson measure on bounded $\mathbb{C}$-convex domains
本文研究了 bounded $\mathbb{C}$-凸域上 Carleson 嵌入算子的有界性和紧性，给出了等价刻画及 sharp $\cB$ 条件。
A berndtsson-Andersson operator solving \bar\partial-equation with W^α-estimates on convex domains of finite type
本文利用Berlesson-Andersson算子和Bergman度量求解了有限型凸区域上满足Carleson条件形式的$\bar\partial$方程，并得到了解的Carleson范数估计.
Suppose $μ$ be a Beltrami coefficient on the unit disk, which is compatible with a convex co-compact Fuchsian group $G$ of the second kind. In this paper we show that if $\displaystyle\frac{|μ|^{2}}{1-|z|^{2}}dxdy $ satisfies the Carleson condition on the infinite boundary boundary of the Dirichlet domain of $G$, then $\displaystyle\frac{|μ|^{2}}{1-|z|^{2}}dxdy$ is a Carleson measure on the unit disk.
In this paper we study Carleson and reverse Carleson measures on holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions in order for a measure $μ$ to be Carleson and reverse Carleson on mixed-normed weighted Bergman spaces.
In this paper, we characterize Carleson measure and vanishing Carleson measure on Bergman spaces with admissible weights in terms of {\it t-Berezin transform} and {\it averaging function} as key tools. Moreover, power bounded and power compact weighted composition operators are characterized as application of Carleson measure and vanishing Carleson measure respectively on Bergman spaces with admissible weights.
We define the notion of $Φ$-Carleson measures where $Φ$ is either a concave growth function or a convex growth function and provide an equivalent definition. We then characterize $Φ$-Carleson measures for Bergman-Orlicz spaces, and apply them to characterize multipliers between Bergman-Orlicz spaces.
On several new results on p-Carleson measures and related measures in the unit disk
我们给出了p-Carleson及相关测度在复平面单位圆盘上的一些新的锐嵌入
Following Semmes and Zinsmeister, we continue the study of Carleson measures and their invariance under pull-back and push-forward operators. We also study the analogous statements for vanishing Carleson measures. As an application, we show that some quotient space of the space of chord-arc curves has a natural complex structure.
The characterization of the Carleson measures for analytic Besov spaces: a simple proof
本文给出了加权解析Besov空间的Carleson测度的特征的一个简单证明。这样的表征提供了一些信息的径向变化的分析Besov函数。
Direct and reverse Carleson measures for $\mathcal{H}(b)$ spaces
本文讨论了de Branges-Rovnyak空间$\mathcal{H}(b)$的正Carleson测度和逆Carleson测度，主要是当b是$H^{\infty}$的单位球的非极值点时.
In this work we study Hardy Sobolev spaces in the ball of $C^n$ with respect to interpolating sequences and Carleson measures. We compare them with the classical Hardy spaces of the ball and we stress analogies and differences.
We provide characterizations of Carleson measures on a certain class of bounded pseudoconvex domains. An example of a vanishing Carleson measure whose Berezin transform does not vanish on the boundary is given in the class of the Hartogs triangles $$\mathbb{H}_{k}:=\left\{ \left(z_{1},z_{2}\right)\in\mathbb{C}^{2}:\left|z_{1}\right|^{k}<\left|z_{2}\right|<1\right\},\;k\in\mathbb{Z}^{+}.$$
We study the Carleson measures associated to the Hardy and weighted Bergman spaces defined on general simply connected domains. This program was initiated by Zinsmeister in his paper \textit{Les domaines de Carleson }(1989), where he shows that the geometry of the domain plays a fundamental role. We will review the classical results presenting, in some cases, alternative proofs and will examine the situation for the weighted Bergman spaces.
We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of integral operators, Cesàro operators and Toeplitz operators, is given using the Carleson measure (or vanishing Carleson measure) characterization.
In this paper, by describing characterizations of Carleson type measures on $[0,1)$, we determine the range of a Cesàro-like operator acting on $H^\infty$. A special case of our result gives an answer to a question posed by P. Galanopoulos, D. Girela and N. Merchán recently.
Let $Ω$ be a Carleson-Denjoy domain and $G$ be its covering group. Let $μ$ be a Beltrami coefficient on the unit disk which is compatible with the group $G$. In this paper we show that if $\frac{|μ|^{2}}{1-|z|^{2}}dxdy$ satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domain of $G$, then $\frac{|μ|^{2}}{1-|z|^{2}}dxdy$ is a Carleson measure on the unit disk. We also show that the above property does not hold for Denjoy domain.
This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model, and de Branges-Rovnyak spaces.
We give a simple proof of the fact that a finite measure $μ$ on the unit disk is a Carleson measure for the Dirichlet space if it satisfies the Carleson one-box condition $μ(S(I))=O(ϕ(|I|))$, where $ϕ:(0,2π]\to(0,\infty)$ is an increasing function such that $\int_0^{2π}(ϕ(x)/x)\,dx<\infty$. We further show that the integral condition on $ϕ$ is sharp.
Carleson measures for weighted Hardy-Sobolev spaces
我们得到了正Borel测度$μ$在$\B^n$上的特征，使得一些加权Hardy-Sobolev嵌入到$L^p(dμ)$中，其中$w$是$\C^n$的单位球面上的$A_p$权.
We introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari anc C. Fefferman are proved.
We study a characterization of slice Carleson measures and of Carleson measures for the both the Hardy spaces $H^p(\mathbb B)$ and the Bergman spaces $\mathcal A^p(\mathbb B)$ of the quaternionic unit ball $\mathbb B$. In the case of Bergman spaces, the characterization is done in terms of the axially symmetric completion of a pseudohyperbolic disc in a complex plane. We also show that a characterization in terms of pseudohyperbolic balls is not possible.
We study the relation between the boundary of a simply connected domain being Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk onto the domain. As an application, we characterize the chord-arc curve with small norm and the asymptotically smooth curve in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.
Carleson measures for weighted holomorphic Besov spaces in $\C^n$
我们得到了$\B^n$上正Borel测度$μ$的特征，使得某些加权全纯Besov空间$B_s^p(w)$嵌入到$L^p(dμ)$中，其中$w$是$\C^n$的单位球上的$B_p$权.
Summing Carleson measure on radial weighted Begman spaces
本文研究了径向加权Bergman空间上正Borel测度诱导的Carleson嵌入的r-求和性质，给出了对所有0<p,q<∞成立的条件。
Reverse Carleson measures in Hardy spaces
给出了单位闭圆盘上的测度$μ$是Hardy空间的逆Carleson测度的一个充要条件.这推广了Lefévre，Li，Queffélec和Rodr\'ıguez-Piazza \cite{LLQR}的一个结果.我们还提供了一个简单的例子表明，类似的Paley-Wiener空间不成立。这个例子可以推广到与单分量内部函数相关联的模型空间。
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。
Decomposition and characterization of VMO via vanishing Carleson measures
本文通过消失Carleson测度建立了VMO的等价表征，证明了VMO函数可分解为连续边界项和与消失Carleson测度相关的积分算子，并通过光滑函数的边界值表征VMO。
Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds
针对 Siegel CR 流形上的 Bernstein 空间，本文刻画 Radon 测度成为 Carleson 测度或采样测度的充要条件，并给出采样序列的充分条件。
Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
本文刻画了双圆盘上Dirichlet空间的Carleson测度，通过建立双参数位势理论并证明强容量不等式，克服了极大原理失效的困难。
Carleson embeddings and pointwise multipliers between Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper half-plane
本文给出涉及凹或凸增长函数的 Carleson 测度的一般刻画，并据此建立上半平面 Hardy-Orlicz 空间与 Bergman-Orlicz 空间之间的连续嵌入与逐点乘子集合的刻画。
Carleson measures for Besov-Sobolev spaces with applications in the unit ball of $C^n$
本文给出了Besov-索伯列夫空间$B_p^σ(B)$的Carleson测度与${\bf C}^n$的单位球上的$p$-Carleson测度之间的关系.作为应用，我们利用$B_p^σ(B)$的Carleson测度刻画了作用在$B_p^σ(B)$空间上的Riemann-Stieltjes算子和乘子.
Compact Carleson measures from sparse sequences
在[1]中，Y.别洛夫河Seip，和作者研究了Carleson措施的某些空间的解析函数的de Branges空间和模型子空间的Hardy空间H2是主要的例子。在本文中，我们继续这一研究路线，通过研究紧凑的Carleson措施，这样的空间。
Reverse Carleson measures for Hardy spaces in the unit ball
本文刻画了单位球Hardy空间的反向Carleson测度，并推导了非内全纯函数对应的de Branges-Rovnyak空间的反向Carleson测度性质。
Given a bounded strongly pseudoconvex domain $D$ in $\mathbb{C}^n$ with smooth boundary, we give a characterization through products of functions in weighted Bergman spaces of $(λ,γ)$-skew Carleson measures on $D$, with $λ>0$ and $γ>1-\frac{1}{n+1}$.
Near-endpoints Carleson Embedding of $\mathcal Q_s$ and $F(p, q, s)$ into tent spaces
本文研究 $\u211a_s$ 与 $F(p, q, s)$ 在端点附近的 Carleson 嵌入问题，利用不同于以往的新方法证明近端点嵌入准则，并验证了相关猜想的微小扰动版本、回答了 Pau 和 Zhao 的公开问题。
Beurling--Carleson Endpoint Counterexamples: Singular Inner Functions and a Semilinear Equation
该论文针对Beurling–Carleson支撑条件的两个端点问题构造反例，揭示了临界支撑条件的必要非充分性，证明结合了Cantor–Moran构造、核发散与非线性能量障碍。
Carleson measures for Hardy-Sobolev spaces in the Siegel upper half-space
针对Siegel上半空间中Arcozzi等人提出的Hardy-Sobolev空间的Carleson测度刻画问题，给出了容型刻画，部分解答了原作者提出的相关问题。
Reverse Carleson Embeddings for Model Spaces
经典的Carleson嵌入定理讨论了单位圆盘上的有限正Borel测度$μ$，其中存在正的常数$c$使得对于所有的$f \in H^2$，单位圆盘的Hardy空间为$|f|_{L^2(μ)} \leq c |f|_{H^2}$. Lefévre等人检查了测量$μ$，其中存在正常数$c$，使得对于所有$f \in H^2$都存在$\|f\|_{L^2(μ)} \geq c |f|_{H^2}$。上述第一种不等式是由Aleksandrov、Baranov、Cohn、Treil和Volberg用模型空间$(ΘH^2)^{\perp}$代替$H^2$来研究的。本文讨论了$(ΘH^2)^{\perp}$中的第二类不等式.
Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains
利用Bergman核Carleson测度刻画了多复变数强伪凸有界域上Bergman空间的Carleson测度，推广了Duren和Weir关于单位球的设定定理.我们还表明，一致离散（相对于小林距离）序列给出的例子Carleson措施，我们计算逃逸到边界的一致离散序列在强伪凸域，推广的结果在单位球由Jevtić，Massaneda和托马斯，杜伦和威尔，和MacCluer。
Carleson Measures and Reproducing Kernel Thesis in Dirichlet-type spaces
本文利用Richter和Sundberg表示定理的推广，给出了Dirichlet型空间$\mathcal D(μ)$的Carleson测度的一个新刻画，当$μ$是有限个点质量和时.在这种情况下，再生核论文结果也成立。
Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls
刻画了多复变数的解析函数的Drury-Arveson-Hardy空间和其它希尔伯特空间的Carleson测度.这为Drury对Von Neumann不等式的推广提供了精确的估计。的表征是在一个几何条件，“分裂树条件”，这反映了各向异性几何基础的Drury-ArvesonHardy空间。
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。
In this note, we obtain a full characterization of radial Carleson measures for the Hilbert-Hardy space on tube domains over symmetric cones. For large derivatives, we also obtain a full characterization of the measures for which the corresponding embedding operator is continuous. Restricting to the case of light cones of dimension three, we prove that by freezing one or two variables, the problem of embedding derivatives of the Hilbert-Hardy space into Lebesgue spaces reduces to the characterization of Carleson measures for Hilbert-Bergman spaces of the upper-half plane or the product of two …
Toeplitz operators and Carleson measures in strongly pseudoconvex domains
研究了n个复变数中有界强伪凸区域D上与有限正Borel测度相关联的Toeplitz算子的映射性质.特别地，我们给出了保证伴随Toeplitz算子将Bergman空间A^p（D）映射到A^r（D）且r>p的严格测度条件，推广了Cuckovic和McNeal的结果，使其更为精确.要做到这一点，我们给出了一个几何特征的Carleson措施和消失Carleson措施的加权Bergman空间的内在小林几何的域，推广到这一设置的结果Kaptanoglu单位球。
We investigate a variant of the Beurling-Ahlfors extension of quasisymmetric homeomorphisms of the real line that is given by the convolution of the heat kernel, and prove that the complex dilatation of such a quasiconformal extension of a strongly symmetric homeomorphism (i.e. its derivative is an ${\rm A}_\infty$-weight whose logarithm is in VMO) induces a vanishing Carleson measure on the upper half-plane.
In this paper, we give a universal description of the boundedness and compactness of Toeplitz operator $\mathcal{T}_μ^ω$ between Bergman spaces $A_η^p$ and $A_\upsilon^q$ when $μ$ is a positive Borel measure, $1<p,q<\infty$ and $ω,η,\upsilon$ are regular weights. By using Khinchin's inequality and Kahane's inequality, we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.
Quaternionic Carleson measures
本文从全纯函数巴拿赫空间出发构造四元数巴拿赫空间（四元数提升），涵盖文献已知例子，主要结果是根据基础全纯函数空间卡尔松测度刻画四元数巴拿赫函数空间的卡尔松测度等，提供统一问题处理方法。
A Rudin-Carleson theorem for multiply connected domains with interpolation
本文利用F.和M. Riesz定理的环域版本，将Rudin-Carleson定理推广到有限连通有界域，并进一步实现了域内有限点插值。
We give in this paper some equivalent definitions of the so called $ρ$-Carleson measures when $ρ(t)=(\log(4/t))^p(\log\log(e^4/t))^q$, $0\le p,q<\infty$. As applications, we characterize the pointwise multipliers on $LMOA(\mathbb S^n)$ and from this space to $BMOA(\mathbb S^n)$. Boundedness of the Cesàro type integral operators on $LMOA(\mathbb S^n)$ and from $LMOA(\mathbb S^n)$ to $BMOA(\mathbb S^n)$ is considered as well.
The purpose of this paper is to establish an atomic decomposition for functions in the weighted mixed norm space $A^{p,q}_ω$ induced by a radial weight $ω$ in the unit disc admitting a two-sided doubling condition. The obtained decomposition is further applied to characterize Carleson measures for $A^{p,q}_ω$, and bounded differentiation operators $D^{(n)}(f)=f^{(n)}$ acting from $A^{p,q}_ω$ to $L^p_μ$, induced by a positive Borel measure $μ$, on the full range of parameters $0<p,q,s<\infty$.
For $0<s<1$, let $\{z_n\}$ be a sequence in the open unit disk such that $\sum_n (1-|z_n|^2)^s δ_{z_n}$ is an $s$-Carleson measure. In this paper, we consider the connections between this $s$-Carleson measure and the theory of Möbius invariant $F(p, p-2, s)$ spaces by the Volterra type operator, the reciprocal of a Blaschke product, and second order complex differential equations having a prescribed zero sequence.
On the Carleson measure criterion in linear systems theory
在Ho，Russell和Weiss中，给出了一维输入元关于对角半群的容许性的Carleson测度准则。我们将他们的结果从希尔伯特空间情形$X=\ell_2$和$L^2$ --容许性推广到更一般的情形$L^p$ --容许性在$\ell_q$ --空间上.在解析对角半群的情形下，我们给出了一个不依赖于拉普拉斯变换方法的新结果。通过对这两个判据的比较，得到了$L^p$ --倒易系统在Curtain意义下的容许性.
Carleson measures on domains in Heisenberg groups
本文研究Heisenberg群中NTA与ADP区域上的Carleson测度，给出基于次椭圆调和函数水平集和$1$-拟共形映射族的两种刻画，并建立平方函数$L^2$界、BMO边界数据估计及Fatou型定理。
Carleson Potentials and the Reproducing Kernel Thesis for Embedding Theorems
本文给出了单位圆盘和单位球上Carleson嵌入定理的一个新证明。证明这一事实的唯一技术工具是格林公式。出发点是每个Carleson测度都产生一个有界的下调和函数。使用这个函数，我们构造了一个新的相关Carleson措施，允许一个简单的嵌入。在圆盘的情况下，这给出了已知的最佳常数，而先前的最佳常数由N给出。尼可斯基
Carleson Measures, Vanishing Mean Oscillation and Critical Points
本文利用有界外函数将有限正 Borel 测度转化为消失 Carleson 测度，并据此构造具有 VMO 边界值且保持 Hardy 空间函数临界点及重数的有界解析函数。
The $\mathcal{Q}_p$ Carleson Measure Problem
设$μ$是开单位圆盘$\mathbb{D}\subset\mathbb{C}$上的非负Borel测度.本文给出了如何判定覆盖$\mathcal{BMOA}$和$\mathcal{B}$的Möbius不变空间$\mathcal{Q}_p$是有界的（分别为，complex）嵌入在二次帐篷型空间$T^\infty_p(μ)$中。有趣的是，嵌入结果可以用来确定有界性（分别为，紧性）和$\mathcal{Q}_p$上的Volterra型和乘法算子。
In this paper, using a new technique from harmonic analysis called sparse domination, we characterize the positive Borel measures including forward, vanishing, and reverse Bergman Carleson measures. The main novelty of this paper is determining the reverse Bergman Carleson measures which have remained open from the work of Luecking [Am. J. Math. 107 (1985) 85-111]. Moreover, in the case of forward and vanishing measures, our results extend the results of [J. Funct. Anal. 280 (2021), no. 6, 108897, 26 pp] from $1\leq p\leq q< 2p$ to all $0<p\leq q<\infty$. In a more general case, we characteriz…
We obtain Littlewood-Paley formulas for Fock spaces $\mathcal{F}^q_{β,ω}$ induced by weights $ω\in A^{restricted}_\infty=\cup_{1\le p<\infty}A^{restricted}_{p}$, where $A^{restricted}_{p}$ is the class of weights such that the Bergman projection $P_α$, on the classical Fock space $\mathcal{F}^2_α$, is bounded on $$\mathcal{L}^p_{α,ω}:=\left\{f:\, \int_{\mathbb{C}}|f(z)|^pe^{-p\fracα{2}|z|^2}\,ω(z)dA(z)<\infty \right\}. $$ Using these equivalent norms for $\mathcal{F}^q_{β,ω}$ we characterize the Carleson measures for weighted Fock-Sobolev spaces $\mathcal{F}^{q,n}_{β,ω}$.
Fock-Sobolev spaces and their Carleson measures
考虑索伯列夫空间$F^{p,m}$由整函数$f$组成，使得$f$的$m$阶导数$f^{(m)}$在Fock空间$F^p$中.证明了整个函数$f$在$F^{p,m}$中当且仅当函数$z^mf(z)$在$F^p$中.刻画了空间$F^{p,m}$的Carleson测度，建立了加权Fock投影在适当的$L^p$空间上的有界性，确定了$F^{p,m}$的Banach对偶，并计算了两个$F^{p,m}$空间之间的复插值空间.
Carleson measures, Riemann-Stieltjes and multiplication operators on a general family of function spaces
设$μ$是复平面单位圆盘上的非负Borel测度.我们刻画了这些测度$μ$，使得包含许多经典函数空间（包括Bloch空间、$BMOA$和$Q_s$空间）的一般解析函数空间族$F(p,q,s)$有界地或紧地嵌入到帐篷型空间$T^{\infty}_{p,s}(μ)$中.这些结果被应用于刻画$F(p,q,s)$上的Riemann-Stieltjes算子和乘法算子的有界性和紧性.
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