A sufficiency condition for the weighted Poincare's type inequality

In this paper, we prove a sufficiency condition on the Poincare's type weighted inequality

\begin{equation} \notag \left(\int _{\Omega }\left|f\right|^{q} \vartheta dx \right)^{1/q} \le C\left(\int _{\Omega }\left|\nabla f\right|^{p} dx \right)^{1/p}, \quad q\geq p>1 \end{equation}
in a convex bounded domain $\Omega$ and general weight function $v\in L^{1,loc}.$