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Shanli Ye

Publications and source records attributed to Shanli Ye.

12 recordsLinked to original sources
arXiv2025

Norm of the Ces\`aro operator between some spaces of analytic functions

In this paper, we determine the exact norm of the Ces\`aro operator $\mathcal{C}$ on the Korenblum space $H^\infty_\alpha$ for $0 < \alpha \leq \frac12$ and on the logarithmically weighted space $H^\infty_{\alpha,\log}$ for $0 < \alpha < 1$. Moreover, we compute its norm when acting from $H^\infty_{\alpha,\log}$ to $H^\infty_\alpha$. Finally, we establish lower and upper bounds for the norm of $\mathcal{C}$ on the $\alpha$-Bloch space $\mathcal{B}^\alpha$ for $\alpha > 1$, and from the Hardy space $H^\infty$ to $\mathcal{B}^\alpha$ for $\alpha\geq 1$.

math.FA↗
arXiv2025

Norm of the Hilbert matrix operator on logarithmically weighted Bloch and Hardy spaces

In this paper, we compute the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ acting from the classical Bloch space $\mathcal{B}$ into the logarithmically weighted Bloch space $\mathcal{B}_{\log}$, and show that it equals $\frac{3}{2}$; we also find that the norm from the space of bounded analytic functions $H^\infty$ into the logarithmically weighted Hardy space $H^{\infty}_{\log}$ is $1$. Furthermore, we establish both lower and upper bounds for the norm of $\mathcal{H}$ when it maps from the $\alpha$-Bloch space $\mathcal{B}^\alpha$ into the logarithmically weighted $\mathcal{B}^\alpha_{\log}$ with $1 <\alpha < 2$, and from the Hardy space $H^{1}$ into the logarithmically weighted Hardy space $H^{1}_{\log}$.

math.FA↗
arXiv2025

Generalized Hilbert operators acting from Hardy spaces to weighted Bergman spaces

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. For $\alpha>0$, the generalized Hankel matrix $\mathcal{H}_{\mu, \alpha}=(\mu_{n, k, \alpha})_{n, k \geq 0}$ with entries $\mu_{n, k, \alpha}=\int_{[0,1)} \frac{\Gamma(n+\alpha)}{n ! \Gamma(\alpha)} t^{n+k} \mathrm{d}\mu(t)$ induces formally the operator \begin{equation*} \mathcal{H}_{\mu, \alpha}(f)(z)=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} \mu_{n, k, \alpha} a_k\right) z^n \end{equation*} on the space of all analytic function $f(z)=\sum_{k=0}^{\infty} a_{k} z^{k}$ in the unit disk $\mathbb{D}$. In this paper, we characterize the measures $\mu$ for which $\mathcal{H}_{\mu, \alpha}(f)$ is well defined on the Hardy spaces $H^p(0 1)$ is a bounded (resp., compact) operator from the Hardy spaces $H^p(0<p<\infty)$ into the weighted Bergman spaces $A_{\alpha-2}^q $.

math.CV↗
arXiv2024

A Derivative-Hilbert operator acting on BMOA space

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu}=(\mu_{n,k})_{n,k\geq 0}$ with entries $\mu_{n,k}=\mu_{n+k}$, where $\mu_{n}=\int_{[0,1)}t^nd\mu(t)$, induces, formally, the Derivative-Hilbert operator $$\mathcal{DH}_\mu(f)(z)=\sum_{n=0}^\infty\left(\sum_{k=0}^\infty \mu_{n,k}a_k\right)(n+1)z^n , ~z\in \mathbb{D},$$ where $f(z)=\sum_{n=0}^\infty a_nz^n$ is an analytic function in $\mathbb{D}$. We characterize the measures $\mu$ for which $\mathcal{DH}_\mu$ is a bounded operator on $BMOA$ space. We also study the analogous problem from the $\alpha$-Bloch space $\mathcal{B}_\alpha(\alpha>0)$ into the $BMOA$ space.

math.FA↗
arXiv2024

Generalized Hilbert Operator Acting on Hardy Spaces

Let $\alpha>0$ and $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu,\alpha}=(\mu_{n,k,\alpha})_{n,k\ge0}$ with entries $\mu_{n,k,\alpha}=\int_{[0,1)}^{}\frac{\Gamma(n+\alpha)}{\Gamma(n+1)\Gamma(\alpha)}t^{n+k}d\mu(t)$, induces, formally, the generalized-Hilbert operator as $$ \mathcal{H}_{\mu,\alpha}\left ( f \right ) \left ( z \right ) =\sum_{n=0}^{\infty} \left (\sum_{k=0}^{\infty} \mu_{n,k,\alpha}a_k \right )z^n,z\in\mathbb{D} $$ where $f(z)={\textstyle \sum_{k=0}^{\infty }} a_kz^k$ is an analytic function in $\mathbb{D}$. This article is devoted study the measures $\mu$ for which $\mathcal{H}_{\mu,\alpha }$ is a bounded(resp., compact) operator from $H^p(0<p\le1)$ into $H^p(1\le q<\infty)$. Then, we also study the analogous problem in the Hardy spaces $H^p(1\le p\le2)$. Finally, we obtain the essential norm of $\mathcal{H}_{\mu,\alpha}$ from $H^p(0<p\le1)$ into $H^p(1\le q<\infty)$.

math.FA↗
arXiv2024

Norm of the Hilbert matrix operator between some spaces of analytic functions

In this paper, we calculate the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ from the logarithmically weighted Korenblum space $H^\infty_{\alpha,\log}$ into Korenblum space $H^\infty_\alpha$, and from the Hardy space $H^\infty$ to the classical Bloch space $\mathcal{B}$. Furthermore, we compute the precise value of the norm on the logarithmically weighted Korenblum space $H^\infty_{\alpha,\log}$, and obtain both the lower and upper bounds of the norm on $\alpha$-Bloch space $\mathcal{B}^{\alpha}$. Finally, in the context of mapping from the Korenblum space $H^\infty_\alpha$ to the $(\alpha+1)$-Bloch space $\mathcal{B}^{\alpha+1}$, we establish the norm of $\mathcal{H}$.

math.FA↗
arXiv2022

Generalized Hilbert Operator Acting on Bloch Type Spaces

Let $μ$ be a positive Borel measure on the interval [0,1). For $α>0$, the Hankel matrix $\mathcal{H}_{μ,α}=(μ_{n,k,α})_{n,k\geq 0}$ with entries $μ_{n,k,α}=\int_{[0,1)}\frac{Γ(n+α)}{n!Γ(α)}t^{n+k}dμ(t)$ formally induces the operator $$\mathcal{H}_{μ,α}(f)(z)=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} μ_{n, k,α} a_{k}\right)z^{n} $$ on the space of all analytic functions $f(z)=\sum_{k=0}^{\infty}a_{k}z^{k}$ in the unit disc $\mathbb{D}$. In this paper, we characterize the measures $μ$ for which $\mathcal{H}_{μ,α}$ ($α\geq 2$) is a bounded (resp., compact) operator from the Bloch type space $\mathscr{B}_β$ ($0<β<\infty$) into $\mathscr{B}_{α-1}$. We also give a necessary condition for which $\mathcal{H}_{μ,α}$ is a bounded operator by acting on Bloch type spaces for general cases.

math.CV↗
arXiv2022

Generalized Hilbert Operator Acting on Weighted Bergman Spaces and on Dirichlet Spaces

Let $μ$ be a positive Borel measure on the interval [0,1). For $β> 0$, The generalized Hankel matrix $\mathcal{H}_{μ,β}= (μ_{n,k,β})_{n,k\geq0}$ with entries $μ_{n,k,β}= \int_{[0.1)}\frac{Γ(n+β)}{n!Γ(β)} t^{n+k}dμ(t)$, induces formally the operator $$\mathcal{H}_{μ,β}(f)(z)=\sum_{n=0}^\infty \left(\sum_{k=0}^\infty μ_{n,k,β}a_k\right)z^n$$ on the space of all analytic function $f(z)=\sum_{k=0}^ \infty a_k z^n$ in the unit disc $\mathbb{D}$. In this paper, we characterize those positive Borel measures on $[0,1)$ such that $\mathcal{H}_{μ,β}(f)(z)= \int_{[0,1)} \frac{f(t)}{(1-tz)^β} dμ(t)$ for all in weighted Bergman Spaces $A_α^p(0 -1)$, and among them we describe those for which $\mathcal{H}_{μ,β}(β>0)$ is a bounded(resp.,compact) operator on weighted Bergman spaces and Dirichlet spaces.

math.CV↗
arXiv2022

A Derivative-Hilbert operator Acting on Dirichlet spaces

Let $μ$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_μ=(μ_{n,k})_{n,k\geq 0}$ with entries $μ_{n,k}=μ_{n+k}$, where $μ_{n}=\int_{[0,1)}t^ndμ(t)$, induces formally the operator as $$\mathcal{DH}_μ(f)(z)=\sum_{n=0}^\infty\left(\sum_{k=0}^\infty μ_{n,k}a_k\right)(n+1)z^n , z\in \mathbb{D},$$ where $f(z)=\sum_{n=0}^{\infty}a_nz^n$ is an analytic function in $\mathbb{D}$. In this paper, we characterize those positive Borel measures on $[0, 1)$ for which $\mathcal{DH}_μ$ is bounded (resp. compact) from Dirichlet spaces $\mathcal{D}_α( 0<α\leq2 )$ into $\mathcal{D}_β( 2\leqβ<4 )$.

math.FA↗
arXiv2022

A Derivative-Hilbert operator acting on Hardy spaces

Let $μ$ be a positive Borel measure on the interval [0,1). The Hankel matrix $\mathcal{H}_μ= (μ_{n,k})_{n,k\geq0}$ with entries $μ_{n,k}= μ_{n+k}$, where $μ_n=\int_{ [0,1)}t^ndμ(t)$, induces formally the operator $$\mathcal{DH}_μ(f)(z)=\sum_{n=0}^\infty (\sum_{k=0}^\infty μ_{n,k}a_k)(n+1)z^n$$ on the space of all analytic function $f(z)=\sum_{k=0}^ \infty a_k z^n$ in the unit disc $\mathbb{D}$. We characterize those positive Borel measures on $[0,1)$ such that $\mathcal{DH}_μ(f)(z)= \int_{[0,1)} \frac{f(t)}{(1-tz)^2} dμ(t)$ for all in Hardy spaces $H^p(0 p$ and $q\geq 1$). We also study the analogous problem in Hardy spaces $H^p(1\leq p\leq 2)$.

math.CV↗