 Thus [$$\begin{split} \label{eq0-0} \int |{{\nabla}}(u\zeta)|^0 {\lesssim}{\left( R^{\frac {0+{\alpha}}0+\frac{{\alpha}-0}{q}} {\|  u \|}_{L^{q}({\widehat{\mathbf A}}_R)}  \right)}^0 + J ^{\frac0{0-{\delta}/0}}.  \end{split}$$]{} To make the right side go to zero, it suffices to find a sequence $R_j\to \infty$, $j\in {{\mathbb N}}$, such that [$$\begin{split} \label{eq0-0} R_j^{\beta}{\|  u \|}_{L^{q}( {\widehat{\mathbf A}}_{R_j})} 