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Haichou Li

Publications and source records attributed to Haichou Li.

13 recordsLinked to original sources
arXiv2026

Hilbertian Hardy--Sobolev Spaces on Tube Domains over Convex Cones

We introduce Hilbertian Hardy--Sobolev spaces on tube domains over convex cones and develop their structural theory from a Fourier-analytic point of view. We first establish a Paley--Wiener type representation, which identifies these spaces with weighted $L^2$ spaces on the dual cone and reveals their intrinsic Fourier structure. This representation leads naturally to a Hardy--Sobolev decomposition theorem for boundary Sobolev spaces on $\mathbb{R}^d$. Building on these structural results, we derive explicit reproducing kernels and characterize Carleson measures for the Hilbertian Hardy--Sobolev spaces. As a preliminary operator-theoretic application, we also derive basic consequences for multipliers and weighted composition operators on these spaces.

math.FA↗
arXiv2026

Banach Hardy-Sobolev Spaces on the Upper Half-plane and Operator Theory

We study Hardy--Sobolev spaces H_n^p(C^+) on the upper half-plane for 1<=p<=infty and n is a nonnegative integer, from both function-theoretic and operator-theoretic viewpoints. We establish an isometric boundary characterization of H_n^p(C^+) via nontangential limits, together with a Sobolev-type embedding theorem, a Cauchy integral representation, a direct-sum decomposition of W_n^p(R) for 1<p<infty, and a generalized Banach algebra structure under pointwise multiplication. We also obtain a finer Fourier-analytic description in the Hilbert case p=2 by proving a Paley--Wiener theorem and deriving the reproducing kernel of H_n^2(C^+).On the operator-theoretic side, we prove the spectral formula for multiplication operators and establish two verifiable sufficient conditions for the boundedness of weighted composition operators. These results provide a systematic theory of Hardy--Sobolev spaces on the upper half-plane beyond the Hilbert setting.

math.FA↗
arXiv2024

Difference of composition operators on Korenblum spaces over tube domain

The Korenblum space, often referred to as a growth space, is a special type of analytic function space. This paper investigates the properties of the difference of composition operators on the Korenblum space over the product of upper half planes, characterizing their boundedness and compactness. Using the result on boundedness, we show that all bounded differences of composition operators are absolutely summable operators.

math.FA↗
arXiv2024

BMO on Weighted Bergman Spaces over Tubular Domains

In this paper, we characterize Bounded Mean Oscillation (BMO) and establish their connection with Hankel operators on weighted Bergman spaces over tubular domains. By utilizing the space BMO, we provide a new characterization of Bloch spaces on tubular domains. Next, we define a modified projection operator and prove its boundedness. Furthermore, we introduce differential operators and demonstrate that these operators belong to Lebesgue spaces on tubular domains. Finally, we establish an integral representation for Bergman functions using these differential operators.

math.CV↗
arXiv2024

Boundedness of Multiparameter Forelli-Rudin Type Operators on Product $L^p$ Spaces over Tubular Domains

In this paper, we introduce and study two classes of multiparameter Forelli-Rudin type operators from $L^{\vec{p}}\left(T_B\times T_B, dV_{\alpha_1}\times dV_{\alpha_2}\right)$ to $L^{\vec{q}}\left(T_B\times T_B, dV_{\beta_1}\times dV_{\beta_2}\right)$, especially on their boundedness, where $L^{\vec{p}}\left(T_B\times T_B, dV_{\alpha_1}\times dV_{\alpha_2}\right)$ and $L^{\vec{q}}\left(T_B\times T_B, dV_{\beta_1}\times dV_{\beta_2}\right)$ are both weighted Lebesgue spaces over the Cartesian product of two tubular domains $T_B\times T_B$, with mixed-norm and appropriate weights. We completely characterize the boundedness of these two operators when $1\le \vec{p}\le \vec{q}<\infty$. Moreover, we provide the necessary and sufficient condition of the case that $\vec{q}=(\infty,\infty)$. As an application, we obtain the boundedness of three common classes of integral operators, including the weighted multiparameter Bergman-type projection and the weighted multiparameter Berezin-type transform.

math.FA↗
arXiv2024

Toeplitz Operators on Weighted Bergman Spaces over Tubular Domains

In this paper, we mainly study the necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators on weighted Bergman spaces over a tubular domains by using the Carlson measures on tubular domains. We also give some related results about Carlson measures.

math.CV↗
arXiv2023

The Extended Paley-Wiener Theorem over the Hardy-Sobolev Spaces

We examine how the square-integrable function subspaces are transformed using the holomorphic Fourier transform. On account of this, the extended Paley-Wiener theorem over the Hardy-Sobolev spaces is produced. The theorem also asserts that the reproducing kernel of the Hardy-Sobolev spaces can be found. We discuss the relationship between the disc and the upper half-plane.

math.FA↗
arXiv2022

Composition Operators on Dirichlet Spaces over the Half-plane

As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains, such as the half-plane. Specifically, we may obtain the rational approximations in the Dirichlet spaces and characterize the composition operators which has dense range on the Dirichlet spaces over the half-plane. Moreover, this paper also considers the relationship between the Dirichlet spaces and Hardy spaces on half-plane.

math.CV↗
arXiv2020

Carleson measures on convex domains

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.

math.CV↗
arXiv2017

Hardy Space Decompositions of $L^p(\mathbb{R}^n)$ for $0<p<1$ with Rational Approximation

This paper aims to obtain decompositions of higher dimensional $L^p(\mathbb{R}^n)$ functions into sums of non-tangential boundary limits of the corresponding Hardy space functions on tubes for the index range $0<p<1$. In the one-dimensional case, Deng and Qian \cite{DQ} recently obtained such Hardy space decomposition result: for any function $f\in L^p(\mathbb{R}),\ 0<p<1$, there exist functions $f_1$ and $f_2$ such that $f=f_1+f_2$, where $f_1$ and $f_2$ are, respectively, the non-tangential boundary limits of some Hardy space functions in the upper-half and lower-half planes. In the present paper, we generalize the one-dimensional Hardy space decomposition result to the higher dimensions, and discuss the uniqueness issue of such decomposition.

math.CV↗