We attempt to relate the domains of partial attraction for sums of i.i.d. random variables to some properties of a generalised regular variation. We give a new characterisation of the domain of partial attraction of the normal distribution and new sufficient conditions for a distribution to belong to a domain of partial attraction.
R. A. Maller. "A Note on Domains of Partial Attraction." Ann. Probab. 8 (3) 576 - 583, June, 1980. https://doi.org/10.1214/aop/1176994727