The shape function describes Fermi motion effects (non perturbative) in sem
i-inclusive heavy flavor decay. Its renormalization properties are substant
ially dependent on the kind of ultraviolet regulator used. For example, the
double logarithm which appears at one loop is larger by a factor 2 in dime
nsional regularization than in lattice regularization. We show that factori
zation of long-distance effects in the shape function is achieved with any
regulator considered.