  We study learning problems in which the underlying class is a bounded subset
of $L_p$ and the target $Y$ belongs to $L_p$. Previously, minimax sample
complexity estimates were known under such boundedness assumptions only when
$p=\infty$. We present a sharp sample complexity estimate that holds for any $p
> 4$. It is based on a learning procedure that is suited for heavy-tailed
problems.
