\Big\|\Big(\int^0_0\sum_{j\in\mathbb{Z}}|F_{j,\,b}^{l}f(x,\,t)|^0{\rm d}t\Big)^{\frac{0}{0}}\chi_{\{|\cdot|>A\}}(\cdot)\Big\|_{L^{p,\,\lambda}(\mathbb{R}^n,\,w)}<\epsilon\|f\|_{L^{p,\,\lambda}(\mathbb{R}^n,\,w)}.\end{aligned}$$ 