Year: 2025
Type: preprint
Abstract: 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 $α\geq 1$.
Source: arXiv (Cornell University)
Authors: Ye, Shanli, Ji, Bin, Zheng, Qisong
Institution: Zhejiang University of Science and Technology
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416435117
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