Carme Cascante, Joaquin M. Ortega
We obtain characterizations of positive Borel measures $μ$ on $\B^n$ so that some weighted holomorphic Besov spaces $B_s^p(w)$ are imbedded in $L^p(dμ)$, where $w$ is a $B_p$ weight in the unit ball of $\C^n$.
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
We give a simple proof of the characterization of the Carleson measures for the weighted analytic Besov spaces. Such characterization provides some information on the radial variation of an analytic Besov function.
This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces $B_p^σ(B)$ and $p$-Carleson measure in the unit ball of ${\bf C}^n$. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on $B_p^σ(B)$ spaces by means of Carleson measures for $B_p^σ(B)$.
We characterize the Carleson measures for the Drury-Arveson Hardy space and other Hilbert spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The characterization is in terms of a geometric condition, the "split tree condition", which reflects the nonisotropic geometry underlying the Drury-Arveson Hardy space.
We define positive Toeplitz operators between harmonic Bergman-Besov spaces $b^p_α$ on the unit ball of $\mathbb{R}^n$ for the full ranges of parameters $0<p<\infty$, $α\in\mathbb{R}$. We give characterizations of bounded and compact Toeplitz operators taking one harmonic Bergman-Besov space into another in terms of Carleson and vanishing Carleson measures. We also give characterizations for a positive Toeplitz operator on $b^{2}_α$ to be a Schatten class operator $S_{p}$ in terms of averaging functions and Berezin transforms for $1\leq p<\infty$, $α\in\mathbb{R}$. Our results extend those kno…
We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers defined in terms of Carleson measures.
The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle "Bergman--type" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov--Sobolev space of analytic functions $B^σ_2$ on the complex ball of $\mathbb{C}^d$. In particular, we demonstrate that for any $σ> 0$, the Carleson measures for the space are ch…
We give several characterizations of holomorphic mean Besov-Lipschitz space on the unit ball in $\cn $ and appropriate Besov-Lipschitz space and prove the equivalences between them. Equivalent norms on the mean Besov-Lipschitz space involve different types of $L^p$-moduli of continuity, while in characterizations of Besov-Lipschitz space we use not only the radial derivative but also the gradient and the tangential derivatives. The characterization in terms of the best approximation by polynomials is also given.
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.
We prove Carleson embeddings for Bergman spaces of tube domains over symmetric cones, we apply them to characterize symbols of bounded Cesàro-type operators from weighted Bergman spaces to weighted Besov spaces. We also obtain Schatten class criteria of Toeplitz operators and Cesàro-type operators on weighted Hilbert-Bergman spaces.
Carleson measures, tent embeddings, and Volterra-type integral operators on the unit ball
本文通过比较Carleson立方体和Bergman度量球条件，结合Berezin型刻画，证明了Besov空间和Bergman空间到对数帐篷空间的嵌入定理，并应用于刻画Volterra型积分算子的有界性、紧性和本质范数。
We use the method of pseudoanalytic continuation to obtain a characterization of spaces of holomorphic functions with boundary values in Besov spaces in terms of polynomial approximations.
A Rudin-Carleson theorem with uniform approximation for manifold-valued maps
本文提出一个针对复流形的鲁丁-卡尔森定理推广，结合插值与均匀逼近，适用于具有孔洞的紧集上的全纯映射。
Properties of Besov and $Q_p$ spaces in terms of the Schwarzian derivative of harmonic mappings
该研究借助Schwarzian导数与Carleson测度刻画单位圆盘内局部单叶保向调和映射的$\text{log }J_f$所属的Besov型与$Q_p$型空间，还引入基于雅可比算子的两类新空间并启动研究。
Fractional order derivative characterizations of Besov-Morrey type spaces with applications
本文通过K-Carleson测度刻画了Besov-Morrey型空间的分数阶导数，推广了Sun等人的结果，并利用n阶导数判据给出线性复微分方程解增长的充分条件。
Approximation in weighted holomorphic Besov spaces in C^n
本文研究多圆柱和单位球中全纯函数的加权 Bergman 与 Besov 空间，寻求非径向权函数的 Mergelyan 型条件以保证函数伸缩按范数收敛且解析多项式在空间中稠密。
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。
On the cyclic behavior of singular inner functions in Besov and sequence spaces
本文证明了单位圆盘上某些Besov型空间中存在循环奇异内函数，给出仅依赖测度光滑模的充分条件，并指出该现象要求测度在所有Beurling-Carleson集上为零质量。
As outlined below, this paper is devoted to a Carleson-type-measure-based study of the holomorphic Campanato $2$-space on the open unit ball $\mathbb B_n$ of $\mathbb C^n$, comprising all Hardy $2$-functions whose oscillations in non-isotropic metric balls on the compact unit sphere $\mathbb S_n$ are proportional to some power of the radius other than the dimension $n\ge 1$.
We consider the weighted $A^p(ω)$ and $B_p(ω)$ spaces of holomorphic functions on the polydisk (in the case of $p>1$). We prove some theorems about the boundedness of Toeplitz operators on weighted Besov spaces $B_p(ω)$ and about the boundedness of generalized little Hankel and Berezin- type operators on $A^p(ω)$.
We introduce the notion of regular (boundary) poles for infinitesimal generators of semigroups of holomorphic self-maps of the unit disc. We characterize such regular poles in terms of $β$-points (i.e. pre-images of values with positive Carleson-Makarov $β$-numbers) of the associated semigroup and of the associated Königs intertwining function. We also define a natural duality operation in the cone of infinitesimal generators and show that the regular poles of an infinitesimal generator correspond to the regular null poles of the dual generator. Finally we apply such a construction to study ra…
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。
We prove that the multiplier algebra of the Drury-Arveson Hardy space $H_{n}^{2}$ on the unit ball in $\mathbb{C}^{n}$ has no corona in its maximal ideal space, thus generalizing the famous Corona Theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach space result: the Besov-Sobolev space $B_{p}^σ$ has the "baby corona property" for all $σ\geq 0$ and $1<p<\infty $. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.
Reverse Carleson measures for spaces of analytic functions
本文定义了拟巴拿赫解析函数空间的$q$-逆Carleson测度，完全刻画了Hardy空间、BMOA空间、Bloch空间等的$q$-逆Carleson测度，并给出了全纯Triebel-Lizorkin空间和Besov空间的相关结果。
Integrable Teichmüller spaces for analysis on Weil-Petersson curves
本文用实p-Besov空间刻画可积Teichmüller空间中的拟对称同胚，建立双全纯对应，证明实解析等价性，并由此表示Weil-Petersson曲线上Besov函数的Cauchy变换。
Assuming that $S$ is the space of functions of regular variation, $ω\in S$, $0< p<\infty$, a function $f$ holomorphic in $B^n$ is said to be of Besov space $B_p(ω)$ if $$\|f\|^p_{B_p(ω)}=\int_{B^n} (1-|z|^2)^p|Df(z)|^p\frac{ω(1-|z|)}{(1-|z|^2)^{n+1}}dν(z) <+\infty,$$ where $dν(z) $ is the volume measure on $B^n$ and $D $ stands for a fractional derivative of $f$. We consider operators on $B_p(ω)$ and show, that they are bounded.
Let $g$ be a holomorphic map of $B$, where $B$ is the unit ball of ${C}^n$. Let $0<p<+\infty, -n-1<q<+\infty$, $q>-1$ and $α>0$. This paper gives some necessary and sufficient conditions for the Extended Ces$\acute{a}$ro Operators induced by $g$ to be bounded or compact between generalized Besov space $B(p,q)$ and $α$- Bloch space ${\mathcal B}^α.$
We provide a full characterization in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by harmonic Bergman-Besov kernels acting between different Lebesgue classes with standard weights on the unit ball of R^{n}. These operators in some sense generalize the harmonic Bergman-Besov projections. To obtain the necessity conditions, we use a technique that heavily depends on the precise inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball. This fruitful technique is new. It has been used first with holom…
We establish an equivalency of the Corona problem (1962) and Gleason problem (1964) in the theory of several complex variables. As an application, we give an affirmative solution of the Corona problem for certain bounded pseudoconvex domains or polydomains including balls and polydiscs. Indeed, we extend our recent work on Gleason problem based on the functional analytic approach, as well as extend recent work of Clos. We also use this equivalency or else other (functional analytic) methods to affirmatively solve both problems for various Banach spaces of bounded holomorphic functions (includi…
We consider the correspondence between the space of $p$-Weil-Petersson curves $γ$ on the plane and the $p$-Besov space of $u=\log γ'$ on the real line for $p >1$. We prove that the variant of the Beurling-Ahlfors extension defined by using the heat kernel yields a holomorphic map for $u$ on a domain of the $p$-Besov space to the space of $p$-integrable Beltrami coefficients. This in particular gives a global real-analytic section for the Teichmüller projection from the space of $p$-integrable Beltrami coefficients to the $p$-Weil-Petersson Teichmüller space.
Simply interpolating and Carleson sequences for Hardy spaces in the polydisc
研究多圆盘Hardy空间简单与通用插值序列关系，指出一维时两者等价，高维时Amar证明$p\boxed{\text{ge}}4$等价，而本文证明$1\boxed{\text{le}}p\boxed{\text{le}}2$时存在简单插值但非通用插值序列。
Similarly to the Bers simultaneous uniformization, the product of the $p$-Weil-Petersson Teichmüller spaces for $p \geq 1$ provides the coordinates for the space of $p$-Weil-Petersson embeddings $γ$ of the real line $\mathbb R$ into the complex plane $\mathbb C$. We prove the biholomorphic correspondence from this space to the $p$-Besov space of $u=\log γ'$ on $\mathbb R$ for $p>1$. From this fundamental result, several consequences follow immediately which clarify the analytic structures concerning parameter spaces of $p$-Weil-Petersson curves. In particular, it follows that the correspondenc…
Beurling-Carleson sets, inner functions and a semi-linear equation
本文综述了Beurling-Carleson集的定义与性质，利用corona型分解揭示了奇异测度的多项性质与该集可数并集的等价关系，并证明了其与半线性方程近最大解的双射对应。
A Sharp Entropy Condition For The Density Of Angular Derivatives
本文证明单位圆盘全纯自映射的有限 Carathéodory 角导数点集在熵可积条件下必为可数个有限熵 Beurling-Carleson 集之并，并构造反例说明该刻画是精确的。
We generalize the Gleason-Kahane-Żelazko theorem to modules. As an application, we show that every linear functional on a Hardy space that is non-zero on outer functions is a multiple of a point evaluation. A further consequence is that every linear endomorphism of a Hardy space that maps outer functions to nowhere-zero functions is a weighted composition operator. In neither case is continuity assumed. We also consider some extensions to other function spaces, including the Bergman, Dirichlet and Besov spaces, the little Bloch space and VMOA.
A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains
本文综述了对称域上全纯函数不变空间的研究，涵盖加权伯格曼空间、Hardy空间等，并重点探讨了Hilbert和半Hilbert空间，同时讨论了最小和最大空间。
Besov-Bergman spaces of $M$-harmonic functions
本文证明单位球上M-调和函数的加权Bergman空间及其解析延拓与Folland研究的Besov型空间一致，给出切向导数刻画，并借助超几何函数平方积分的渐近估计分析了其与Sobolev空间的关系。
A particular consequence of the famous Carleson-Hunt theorem is that the Taylor series expansions of bounded holomorphic functions on the open unit disk converge almost everywhere on the boundary, whereas on single points the convergence may fail. In contrast, Bayart, Konyagin, and Queffélec constructed an example of an ordinary Dirichlet series $\sum a_n n^{-s}$, which on the open right half-plane $[Re >0]$ converges pointwise to a bounded, holomorphic function -- but diverges at each point of the imaginary line, although its limit function extends continuously to the closed right half plane.…
$A^p_α$ classes in the Dirichlet range: inner-outer factorization, Carleson measures and weak products
本文研究了Dirichlet范围内$A^p_α$空间的性质，证明当$p≠2$且$p>1/2$时，$A^p_α$不是向量空间，且范数不随$p$增加而单调递增。
We study the holomorphic tent spaces $\mathcal{HT}^p_{q,α}(\Bn)$, which are motivated by the area function description of the Hardy spaces on one hand, and the maximal function description of the Hardy spaces on the other. Characterizations for these spaces under general fractional differential operators are given. We describe the dual of $\mathcal{HT}^p_{q,α}(\Bn)$ for the full range $0<p,q<\infty$ and $α>-n-1$. Here the case $1<p<\infty$, $q\leq 1$ leads us to the Hardy-Bloch type spaces $\mathcal{BT}^{p}(\Bn)$ and $\mathcal{BT}^{p,0}(\Bn)$, the latter being the predual of $\mathcal{HT}^p_{1…
We study a Toeplitz type operator $Q_μ$ between the holomorphic Hardy spaces $H^p$ and $H^q$ of the unit ball. Here the generating symbol $μ$ is assumed to a positive Borel measure. This kind of operator is related to many classical mappings acting on Hardy spaces, such as composition operators, the Volterra type integration operators and Carleson embeddings. We completely characterize the boundedness and compactness of $Q_μ:H^p\to H^q$ for the full range $1<p,q<\infty$; and also describe the membership in the Schatten classes of $H^2$. In the last section of the paper, we demonstrate the usef…
Let $\mathcal{D}$ be the classical Dirichlet space, the Hilbert space of holomorphic functions on the disk. Given a holomorphic symbol function $b$ we define the associated Hankel type bilinear form, initially for polynomials f and g, by $T_{b}(f,g):= < fg,b >_{\mathcal{D}} $, where we are looking at the inner product in the space $\mathcal{D}$. We let the norm of $T_{b}$ denotes its norm as a bilinear map from $\mathcal{D}\times\mathcal{D}$ to the complex numbers. We say a function $b$ is in the space $\mathcal{X}$ if the measure $dμ_{b}:=| b^{\prime}(z)| ^{2}dA$ is a Carleson measure for $\m…
Let $μ$ be a positive finite measure on the unit circle. The Dirichlet type space $\mathcal{D}(μ)$, associated to $μ$, consists of holomorphic functions on the unit disc whose derivatives are square integrable when weighted against the Poisson integral of $μ$. First, we give an estimate of the norm of the reproducing kernel $k^μ$ of $\mathcal{D}(μ)$. Next, we study the notion of $μ$-capacity associated to $\mathcal{D}(μ)$, in the sense of Beurling--Deny. Namely, we give an estimate of $μ$-capacity of arcs in terms of the norm of $k^μ$. We also provide a new condition on closed sets to be $μ$-p…
Riesz-Kolmogorov type compactness criteria in function spaces with applications
本文提出适用于多种函数空间的Riesz-Kolmogorov型紧性准则，并用于刻画Bergman空间上的紧Toeplitz算子及推导Hardy空间上Hankel算子的紧性。
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。