Year: 2023
Type: preprint
Abstract: Let $μ$ be a finite positive Borel measure on the interval $[0, 1)$ and $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n} \in H(\mathbb{D})$. The Cesàro-like operator is defined by $$ \mathcal {C}_μ (f)(z)=\sum^\infty_{n=0}\left(μ_n\sum^n_{k=0}a_k\right)z^n, \ z\in \mathbb{D}, $$ where, for $n\geq 0$, $μ_n$ denotes the $n$-th moment of the measure $μ$, that is, $μ_n=\int_{[0, 1)} t^{n}dμ(t)$. Let $X$ and $Y$ be subspaces of $H( \mathbb{D})$, the purpose of this paper is to study the action of $\mathcal {C}_μ$ on distinct pairs $(X, Y)$. The spaces considered in this paper are Hardy space $H^{p}(0
Source: arXiv (Cornell University)
Author: Tang, Pengcheng
Institution: Hunan Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4376864969