arXiv subjects

Thai Thuan Quang

Publications and source records attributed to Thai Thuan Quang.

6 recordsLinked to original sources

arXiv2025

Characterizing Weighted Composition Operators on Weighted-Type High-Order Growth Spaces via the Component Function $φ_p$

Let $ψ$ be a holomorphic function on the open unit ball $\BB \subset \C^N$, and let $φ$ be a holomorphic self-map of $\BB$, associated with normal weights $ν$ and $μ$. We consider the weighted composition operator $ W_{ψ,φ} : \mathcal H_ν^{(n)} \to \mathcal H_μ^{(m)}, \quad n,m \in \N,$ acting between weighted-type high-order growth spaces. Unlike previous studies that involve the full symbol $φ$, this paper establishes characterizations of the boundedness, compactness, and asymptotic norm estimates of $W_{ψ,φ}$ \emph{solely in terms of the symbol $ψ$ and a single component function $φ_p$ of $φ$}, offering a new approach to the analysis of such operators.

math.CV↗

arXiv2022

Extended Cesàro composition operators on weak Bloch-type spaces on the unit ball of a Hilbert space

Denote by $ B_X $ the unit ball of an infinite-dimensional complex Hilbert space $ X. $ Let $ψ\in H(B_X),$ the space of all holomorphic functions on the unit ball $B_X,$ $φ\in S(B_X)$ the set of holomorphic self-maps of $B_X. $ Let $C_{ψ, φ}: \mathcal B_ν(B_X)$ (and $ \mathcal B_{ν,0}(B_X)$) $\to \mathcal B_μ(B_X) $ (and $ \mathcal B_{μ,0}(B_X)$) be weighted extended Cesàro operators induced by products of the extended Cesàro operator $ C_φ$ and integral operator $T_ψ.$ In this paper, we characterize the boundedness and compactness of $ C_{ψ,φ} $ via the estimates for the restrictions of $ ψ$ and $ φ$ to a $ m$-dimensional subspace of $ X $ for some $ m\ge2. $ Based on these we give necessary as well as sufficient conditions for the boundednees, the (weak) compactness of $ \widetilde{C}_{ψ, φ} $ between spaces of Banach-valued holomorphic functions weak-associated to $ \mathcal B_ν(B_X) $ and $ \mathcal B_μ(B_X). $

math.CV↗

arXiv2022

Weighted composition operators on weak holomorphic spaces and application to weak Bloch-type spaces on the unit ball of a Hilbert space

Let $ E $ be a space of holomorphic functions on the unit ball $ B_X $ of a Banach space $ X.$ In this work, we introduce a Banach structure associated to $ E $ on the linear space $ WE(Y) $ containing $ Y$-valued holomorphic functions on $ B_X $ such that $ w \circ f \in E $ for every $ w \in W, $ a separating subspace of the dual $ Y' $ of a Banach $ Y. $ We establish the relation between the boundedness, the (weak) compactness of the weighted composition operators $ W_{ψ,φ}: f\mapsto ψ\cdot(f \circ φ) $ on $ E $ and $ \widetilde{W}_{ψ,φ}: g\mapsto ψ\cdot(g \circ φ) $ on $ WE(Y)$ via some characterizations of the separating subspace $ W. $ As an application, via the estimates for the restrictions of $ ψ$ and $ φ$ to a $ m$-dimensional subspace of $ X $ for some $ m\ge2, $ we characterize the properties mentioned above of $ W_{ψ,φ} $ on Bloch-type spaces $ \mathcal B_μ(B_X) $ of holomorphic functions on the unit ball $ B_X $ of an infinite-dimensional Hilbert space as well as their the associated spaces $W\mathcal B_μ(B_X,Y), $ where $ μ$ is a normal weight on $ B_X. $

math.FA↗

arXiv2019

Fréchet-valued formal power series

Let $A$ be a non-projectively-pluripolar set in a Fréchet space $E.$ We give sufficient conditions to ensure the convergence on some zero-neighbourhood in $E$ of a (sequence of) formal power series of Fréchet-valued continuous homogeneous polynomials provided that the convergence holds at a zero-neighbourhood of each complex line $\ell_a := \C a$ for every $a \in A.$

math.CV↗

arXiv2017

Hausdorff operators on holomorphic Hardy spaces and applications

The aim of this paper is to characterize the nonnegative functions $φ$ defined on $(0,\infty)$ for which the Hausdorff operator $$\mathscr H_φf(z)= \int_0^\infty f\left(\frac{z}{t}\right)\frac{φ(t)}{t}dt$$ is bounded on the Hardy spaces of the upper half-plane $\mathcal H_a^p(\mathbb C_+)$, $p\in[1,\infty]$. The corresponding operator norms and their applications are also given.

math.CA↗

arXiv2017

Norm of the Hausdorff operator on the real Hardy space $H^1(\mathbb R)$

Let $φ$ be a nonnegative integrable function on $(0,\infty)$. It is well-known that the Hausdorff operator $\mathcal H_φ$ generated by $φ$ is bounded on the real Hardy space $H^1(\mathbb R)$. The aim of this paper is to give the exact norm of $\mathcal H_φ$. More precisely, we prove that $$\|\mathcal H_φ\|_{H^1(\mathbb R)\to H^1(\mathbb R)}= \int_0^\infty φ(t)dt.$$

math.CA↗