Cesàro-type operators on average radial integrability spaces induced by doubling weights

In this paper, we study the Cesàro-type operator $${\text{Ces}}_{\mu ,\beta }f(z)={\int }_{[0,1)}\frac{f(tz)}{(1-tz{)}^{\beta }}d\mu (t),$$ where $\mu$ is a positive Borel measure on $[0,1)$ and $\beta >0$. For $0<p,q<\mathrm{\infty }$ and radial doubling weights ${\omega }_1,{\omega }_2$, we prove that ${\text{Ces}}_{\mu ,\beta }:{\text{AL}}_p^q({\omega }_1)\to {\text{AL}}_p^q({\omega }_2)$ is bounded if and only if $$\mu ([0,1))+\underset{1\mathrm{/}2\le r<1}{\sup }\frac{\mu ([r,1))}{(1-r{)}^{\beta }}{\left(\frac{\text{what}{\omega }_2(r)}{\text{what}{\omega }_1(r)}\right)}^{1\mathrm{/}p}<\mathrm{\infty },$$ and its norm is comparable to this quantity. For standard weights, our result extends \cite{BlascoMas2026,GalanopoulosSiskakisZhao2025} to the full range $0<p=q<\mathrm{\infty }$. We further characterize compactness and the essential norm on average radial integrability spaces induced by doubling weights.