Extended Ces$\acute{a}$RO Operators between Generalized Besov Spaces and Bloch Type Spaces in the Unit Ball

TL;DR

This paper characterizes when Extended Cesàro Operators, induced by holomorphic maps, are bounded or compact between generalized Besov spaces and Bloch type spaces in the unit ball.

Contribution

It provides necessary and sufficient conditions for the boundedness and compactness of these operators between specific function spaces.

Findings

Derived criteria for boundedness of operators

Established conditions for compactness of operators

Enhanced understanding of operator behavior in complex analysis

Abstract

Let $g$ be a holomorphic map of $B$, where $B$ is the unit ball of ${C}^n$. Let $0<p<+\infty, -n-1<q<+\infty$, $q>-1$ and $\alpha>0$. This paper gives some necessary and sufficient conditions for the Extended Ces$\acute{a}$ro Operators induced by $g$ to be bounded or compact between generalized Besov space $B(p,q)$ and $\alpha$- Bloch space ${\mathcal B}^\alpha.$