Qisong Zheng | Searcharxiv

arXiv2026

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 $α$-Bloch space $\mathcal{B}^α$ into the logarithmically weighted $\mathcal{B}^α_{\log}$ with $1 <α< 2$, and from the Hardy space $H^{1}$ into the logarithmically weighted Hardy space $H^{1}_{\log}$.

math.FA↗

arXiv2025

Norm of the Cesàro operator between some spaces of analytic functions

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

math.FA↗