Partial integral operators of non-negative orders in weighted Lebesgue spaces

We study a weighted partial integral operator in a weighted Lebesgue space $L_p^{\gamma}(D)$ with a measure of integration $d\mu_\gamma(x)=x^\gamma dx$ in $\mathbb{R}_2 $ and $\mathbb{R}_n$. The concept of the order of a weighted partial integral operator is introduced. A sufficient condition for such operators to be bounded in $L_p^\gamma$ is obtained.