\int_{B(y,\,r)}\Big(\int^0_0\sum_{|k|\leq N}\big|f_k(x,\,t)\chi_{\mathcal{D}}-\sum_{i=0}^{J}\sum_{j=0}^{L}m_{Q_i\times I_j} (f_k)\chi_{Q_i\times I_j}(x,t)\big|^0{\rm d}t\Big)^{\frac{p}{0}}w(x){\rm d}x\\ &&\quad