Guantie Deng

activity

20112022

1 < p < \infty

) over Lipschitz Domains

1 citations · 1 across the 14 of their papers we have counts for

collaborators

14 papers

math.CV2022

The weighted reproducing kernels of the Reinhardt domain

Qian Fu, Guantie Deng

In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain con…

math.CV2022

$L^{p}$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $C^{n + 1}$

Qian Fu, Guantie Deng

In this paper, we investigate a class of domains $Ω_{γ}^{n + 1} = {(z, w) \in C^{n} \times C : ∣ z ∣^{γ} < ∣ w ∣ < 1}$ for $γ > 0$ that generalizes the Hartogs triangle. We obtain a…

math.CV2022

$L^{p}$ regularity of the Bergman projection on generalizations of the Hartogs triangle in $C^{n + 1}$

Qian Fu, Guan-Tie Deng, Hui Cao

In this paper we investigate a class of domains $Ω_{k}^{n + 1} = {(z, w) \in C^{n} \times C : ∣ z ∣^{k} < ∣ w ∣ < 1}$ for $k \in Z^{+}$ which generalizes the Hartogs tria…

math.CV2020

Phase Retrieval in Hardy Space

Wei Qu, Xiao-Yun Sun, Guan-Tie Deng

This paper concerns the study of reconstructing a function $f$ in the Hardy space of the unit disc $\D$ from intensity measurements $|f(z)|,\ z\in \D.$ It's known as the problem of…

math.CV2020

Reproducing kernels of some weighted Bergman spaces

Guan-Tie Deng, Yun Huang, Tao Qian

Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergma…

math.CA2020

Sparse Approximation to the Dirac-δ Distribution

Wei Qu, Tao Qian, Guan-Tie Deng

The Dirac-δ distribution may be realized through sequences of convlutions, the latter being also regarded as approximation to the identity. The present study proposes the so called…

math.CV2020

A sufficient condition for n-Best Kernel Approximation in Reproducing Kernel Hilbert Spaces

Wei Qu, Tao Qian, Guan-Tie Deng

We show that if a reproducing kernel Hilbert space $H_{K},$ consisting of functions defined on $E,$ enjoys Double Boundary Vanishing Condition (DBVC) and Linear Independent Con…

math.CV2017

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

Guantie Deng, Haichou Li, Tao Qian

This paper aims to obtain decompositions of higher dimensional $L^{p} (R^{n})$ functions into sums of non-tangential boundary limits of the corresponding Hardy space functions…

math.CV2017

Hardy Spaces over Half-strip Domains

Guantie Deng, Rong Liu

We define Hardy spaces $H^{p} (Ω_{\pm})$ on half-strip domain~ $Ω_{+}$ and $Ω_{-} = C ∖ Ω_{+}$ , where $0 < p < \infty$ , and prove that functions in $H^{p} (Ω_{\pm})$ has non-ta…

math.CV2017

Notes of Boundedness on Cauchy Integrals on Lipschitz Curves ( $p = 2$ )

Guantie Deng, Rong Liu

We provide the details of the first proof in~\cite{CJS89}, which proved that Cauchy transform of $L^{2}$ ~functions on Lipschitz curves is bounded. We then prove that every $L^{2}$ ~func…

math.CV2017★ 1 cited

Hardy Spaces ( $1 < p < \infty$ ) over Lipschitz Domains

Guantie Deng, Rong Liu

Let $Γ$ be a Lipschitz curve on the complex plane $C$ and $Ω_{+}$ is the domain above $Γ$ , we define Hardy space $H^{p} (Ω_{+})$ as the set of holomorphic functions $F$ satisfyin…

math.CV2015

Rational Approximation, Hardy Space - Decomposition of Functions in $L_{p}, p < 1$ : Further Results in Relation to Fourier Spectrum Characterization of Hardy Spaces

Guantie Deng, Tao Qian

Subsequent to our recent work on Fourier spectrum characterization of Hardy spaces $H^{p} (R)$ for the index range $1 \leq p \leq \infty,$ in this paper we prove further result…

math.CA2012

Criterions of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schrödinger operator in a cone

Pinhong Long, Zhiqiang Gao, Guantie Deng

In the paper we give some criterions for a-minimally thin sets and a-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or {\infty}…

math.CV2011

Clarkson-Erdös-Schwartz Theorem on a Sector

Guan-Tie Deng

We prove a Clarkson-Erdös-Schwartz type theorem for the case of a closed sector in the plane. Concretely, we get some sufficient conditions for the incompleteness and minimality of…

The weighted reproducing kernels of the Reinhardt domain

Lp boundedness of the Bergman Projection on generalizations of the Hartogs triangle in Cn+1

Lp regularity of the Bergman projection on generalizations of the Hartogs triangle in Cn+1

Phase Retrieval in Hardy Space

Reproducing kernels of some weighted Bergman spaces

Sparse Approximation to the Dirac-δ Distribution

A sufficient condition for n-Best Kernel Approximation in Reproducing Kernel Hilbert Spaces

Hardy Space Decompositions of Lp(Rn) for 0<p<1 with Rational Approximation

Hardy Spaces over Half-strip Domains

Notes of Boundedness on Cauchy Integrals on Lipschitz Curves (p=2)

Hardy Spaces (1<p<∞) over Lipschitz Domains

Rational Approximation, Hardy Space - Decomposition of Functions in Lp​,p<1: Further Results in Relation to Fourier Spectrum Characterization of Hardy Spaces

Criterions of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schrödinger operator in a cone

Clarkson-Erdös-Schwartz Theorem on a Sector

$L^{p}$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $C^{n + 1}$

$L^{p}$ regularity of the Bergman projection on generalizations of the Hartogs triangle in $C^{n + 1}$

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

Notes of Boundedness on Cauchy Integrals on Lipschitz Curves ( $p = 2$ )

Hardy Spaces ( $1 < p < \infty$ ) over Lipschitz Domains

Rational Approximation, Hardy Space - Decomposition of Functions in $L_{p}, p < 1$ : Further Results in Relation to Fourier Spectrum Characterization of Hardy Spaces