  We extend the subrepresentation formula $$ |f(x)|\le c_n\,I_1(|\nabla f|)(x)
$$ in several ways. First, we consider more general $A_1$-potential operators
on the right-hand side and prove local and global pointwise inequalities for
these operators. Second, we show that we can improve the right-hand side using
fractional derivatives. Finally, we extend our results to rough singular
integral operators, similar to the main result in [HMP1].
