A one-sided large deviation local limit theorem

We establish a one-sided large deviation local limit theorem for sums of i.i.d. rv's with heavy tails assuming only a condition on the one-sided tail of the generic distribution. The results in [Baltrunas, A., 1996. A local limit theorem on one-sided large deviations for dominated-variation distributions. Lithuanian Math. J. 36, 1-7] are improved and thus, the result in [Doney, R.A., 1989. A large deviation local limit theorem. Math. Proc. Cambridge Philos. Soc. 105, 575-577] is generalized.