Let $1\leq p<\infty$. Prove that there exists $C>0$ such that $$ \left(\int\left|\sum_{i=1}^\infty a_i\chi_{2Q_i}\right|^p \, dx\right)^{1/p} \leq C\left(\int\left|\sum_{i=1}^\infty |a_i|\chi_{Q_i}\right|^p \, dx\right)^{1/p}. $$ Here $\{a_i\}$ is a sequence of real numbers and $\{Q_i\}$ is a sequence of cubes in $\mathbb{R}^n$, $2Q_i$ is the cube with the same center as $Q_i$ but twice its length.
How to prove this? Thanks.