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

In this paper, we study the Cesàro-type operator $$ \Ces_{μ,β}f(z)=\int_{[0,1)}\frac{f(tz)}{(1-tz)^β}\,dμ(t), $$ where \(μ\) is a positive Borel measure on \([0,1)\) and \(β>0\). For \(0<p,q<\infty\) and radial doubling weights \(ω_1,ω_2\), we prove that \(\Ces_{μ,β}:\AL_p^q(ω_1)\to\AL_p^q(ω_2)\) is