= Solution
One useful form of the <Simon absorption lemma> is the following. Let $S$ be nonnegative and subadditive on balls contained in $B_R$, and suppose that for every such $B_r$,
$$
r^\gamma S(B_{r/2})
\leq\varepsilon r^\gamma S(B_r)+A(B_r),
$$
where $A$ is also subadditive and $\varepsilon$ is smaller than a constant depending only on $n$ and $\gamma$. Then
$$
R^\gamma S(B_{R/2})\leq C A(B_R).
$$
More generally, an additional controlled remainder on the right remains with a dimensional constant. The proof covers $B_{R/2}$ by finitely many smaller balls, sums by subadditivity, and iterates so that the $S$ term is absorbed.
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