In this paper, we give a necessary and sufficient condition on Hardy's integral inequality: \begin{equation}\label{ort_cond} \int_{X}[Tf]^{p}wd\mu \leq C\int_{X}f^{p}vd\mu\;\;\;\;\;\forall f \geq 0 \end{equation} where $w, v$ are non-negative measurable functions on $X$, a non-negative function $f$ defined on $(0, \infty), K(x,y)$ is a non-negative and measurable on $X \times X$, $(Tf)(x)= \int^{\infty}_{0}K(x,y)f(y)dy $ and $C$ is a constant depending on $K, p$ but independent of $f$. This work is a continuation of our recent result in \cite{RauGVM1}.