Let p∈(0,1] and s≥[ n(1/ p−1)], where [ n(1/ p−1)] denotes the maximal integer no more than n(1/ p−1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H p(ℝ n) to some quasi-Banach space ℬ if and only if T maps all ( p,2, s)-atoms into uniformly bounded elements of ℬ.