2000 character limit reached
Cesàro-like operator acting between Bloch type spaces (2208.11921v3)
Published 25 Aug 2022 in math.FA
Abstract: Let $\mu$ 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 Ce`{a}sro-like operator is defined by $$ \mathcal{C}\mu(f)(z)=\sum\infty{n=0}\mu_n\left(\sumn_{k=0}a_k\right)zn, \ z\in \mathbb{D}, $$ where, for $n\geq 0$, $\mu_n$ denotes the $n$-th moment of the measure $\mu$, that is, $\mu_n=\int_{[0, 1)} t{n}d\mu(t)$. In this paper, we characterize the measures $\mu$ for which $\mathcal{C}_\mu$ is bounded (compact) from one Bloch type space, $\mathcal {B}{\alpha}$, into another one, $\mathcal {B}{\beta}$.