Solution
= Solution
The kernel is globally Lipschitz with constant $1/\delta^2$: this holds on each of its linear pieces, and summing across the finitely many intervening breakpoints proves it across pieces as well. Consequently
$$
\boxed{|(f*g)(t_1)-(f*g)(t_2)|\leq\int|f(s)|\frac{|t_1-t_2|}{\delta^2}ds=\|f\|_1\frac{|t_1-t_2|}{\delta^2}.}
$$