Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 107 / 1 / c

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 $B_r$,where $A$ is also subadditive and $\epsilon$ is smaller than a constant depending only on $n$ and $\gamma$. ThenMore 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.