(\mathbb{R}^n,\,w)}<\epsilon;$$  -   for each fixed $\epsilon>0$ and $N\in\mathbb{N}$, there exists a constant $\varrho>0$, such that for all $\{f_k\}_{k\in\mathbb{Z}}\in \mathcal{G}$, $$\Big\|\sup_{|h|\leq \varrho}\Big(\int^0_0     \sum_{|k|\leq N}|f_k(