A Cesàro-like operator from a class of analytic function spaces to analytic Besov spaces

Abstract Let $\mu $ be a finite positive Borel measure on $[0,1)$ and $f(z)=\sum _{n=0}^{\infty }a_{n}z^{n} \in H(\mathbb {D})$ . For $0<\alpha <\infty $ , the generalized Cesàro-like operator $\mathcal {C}_{\mu ,\alpha }$ is defined by $$ \begin{align*}\mathcal {C}_{\mu,\alpha}(f)(z)=\sum^\infty_{n=0}\left(\mu_n\sum^n_{k=0}\frac{\Gamma(n-k+\alpha)}{\Gamma(\alpha)(n-k)!}a_k\right)z^n, \ z\in \mathbb{D}, \end{align*} $$ where, for $n\geq 0$ , $\mu _n$ denotes the n th moment of the measure $\mu $ , that is, $\mu _n=\int _{0}^{1} t^{n}d\mu (t)$ . For $s>1$ , let X be a Banach subspace of $H(\mathbb {D})$ with $\Lambda ^{s}_{\frac {1}{s}}\subset X\subset \mathcal {B}$ . In this article, for $1\leq p <\infty $ , we characterize the measure $\mu $ for which $\mathcal {C}_{\mu ,\alpha }$ is bounded (resp. compact) from X into the analytic Besov space $B_{p}$ .