BMO and Hankel operators on Bergman space of the Siegel upper half-space

Hankel Operators and Weak Factorization for Hardy-Orlicz Spaces

We study the holomorphic Hardy-Orlicz spaces H^Φ(Ω), where Ωis the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function Φis in particular such that H ^1(Ω) \subset H^Φ(Ω) \subset H ^p (Ω) for some p > 0. We develop for them maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Omega). As a consequence, we characterize those Hankel operators which are bounded from H ^Φ(Ω) into H^1 (Ω).

Cauchy-Szegö operator, quaternionic Siegel upper half space, commutator, weighted Morrey space

In the setting of quaternionic Heisenberg group $\mathscr H^{n-1}$, we characterize the boundedness and compactness of commutator $[b,\mathcal C]$ for the Cauchy--Szegö operator $\mathcal C$ on the weighted Morrey space $L_w^{p,\,κ}(\mathscr H^{n-1})$ with $p\in(1, \infty)$, $κ\in(0, 1)$ and $w\in A_p(\mathscr H^{n-1}).$ More precisely, we prove that $[b,\mathcal C]$ is bounded on $L_w^{p,\,κ}(\mathscr H^{n-1})$ if and only if $b\in {\rm BMO}(\mathscr H^{n-1})$. And $[b,\mathcal C]$ is compact on $L_w^{p,\,κ}(\mathscr H^{n-1})$ if and only if $b\in {\rm VMO}(\mathscr H^{n-1})$.

Duality theorems for coinvariant subspaces of $H^1$

Let $θ$ be an inner function satisfying the connected level set condition of B. Cohn, and let $K^{1}_θ$ be the shift-coinvariant subspace of the Hardy space $H^1$ generated by $θ$. We describe the dual space to $K^{1}_θ$ in terms of a bounded mean oscillation with respect to the Clark measure $σ_α$ of $θ$. Namely, we prove that $(K^{1}_θ \cap zH^1)^* = {\rm BMO}(σ_α)$. The result implies a two-sided estimate for the operator norm of a finite Hankel matrix of size $n\times n$ via ${\rm BMO}(μ_{2n})$-norm of its standard symbol, where $μ_{2n}$ is the Haar measure on the group $\{ξ\in \mathbb{C}:…

加权 Hardy 空间上 Hankel 算子的再生核命题

Reproducing Kernel Thesis of Hankel Operators on Weighted Hardy Spaces

本文研究了带 Muckenhoupt 权的两加权空间间 Hankel 算子的有界性，提出双权版 Garsia 范数，证明在再生核上测试足以判定算子有界性，并证明了 Carleson 嵌入定理的双权版本。

Hankel算子的强再生核定理与Garsia范数

The strong reproducing kernel thesis for Hankel operators and the Garsia norm

本文针对再生核希尔伯特空间上的有界算子提出强再生核定理（SRKT）的判定问题，并具体研究Hardy空间上Hankel算子满足SRKT的条件，同时探讨BMO单位球在Garsia范数下的几何性质。

具有倍权函数的Bergman空间上的Toeplitz和Hankel算子

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。

作用于BMOA空间的导数-希尔伯特算子

A Derivative-Hilbert operator acting on BMOA space

本文刻画了使导数-希尔伯特算子有界于BMOA空间的测度条件，并研究了从α-Bloch空间到BMOA空间的类似问题。

Volterra operators on Hardy spaces of Dirichlet series

For a Dirichlet series symbol $g(s) = \sum_{n \geq 1} b_n n^{-s}$, the associated Volterra operator $\mathbf{T}_g$ acting on a Dirichlet series $f(s)=\sum_{n\ge 1} a_n n^{-s}$ is defined by the integral $f\mapsto -\int_{s}^{+\infty} f(w)g'(w)\,dw$. We show that $\mathbf{T}_g$ is a bounded operator on the Hardy space $\mathcal{H}^p$ of Dirichlet series with $0 < p < \infty$ if and only if the symbol $g$ satisfies a Carleson measure condition. When appropriately restricted to one complex variable, our condition coincides with the standard Carleson measure characterization of ${\operatorname{BMOA…

A generalized Hilbert operator acting on conformally invariant spaces

If $μ$ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_μ$ be the Hankel matrix $\mathcal H_μ=(μ_{n, k})_{n,k\ge 0}$ with entries $μ_{n, k}=μ_{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $μ_n$ denotes the moment of orden $n$ of $μ$. This matrix induces formally the operator $$\mathcal{H}_μ(f)(z)= \sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} μ_{n,k}{a_k}\right)z^n$$ on the space of all analytic functions $f(z)=\sum_{k=0}^\infty a_kz^k$, in the unit disc $\D $. This is a natural generalization of the classical Hilbert operator. The action of the operators $H_{μ}$ on Hardy s…