Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions

This paper broadens the range on which Fouvry and Radziwiłł's results on nearly balanced convolutions apply. In particular, let $α_m$ and $β_n$ be sequences supported on $m\sim M$ and $n\sim N$ where $β_n$ is equidistributed for small moduli, and let $Q=X^{\frac 12+\varepsilon}$. We find that \begin