Let 1 ≤ p< 2 and 0 < α, β< ∞ with 1 / p= 1 / α+ 1 / β. Let { Xn, n≥ 1 } be a sequence of random variables satisfying a generalized Rosenthal type inequality and stochastically dominated by a random variable X with E| X| β< ∞. Let { an k, 1 ≤ k≤ n, n≥ 1 } be an array of constants satisfying ∑k=1n|ank|α=O(n). Marcinkiewicz–Zygmund type strong laws for weighted sums of the random variables are established. Our results generalize or improve the corresponding ones of Wu (J. Inequal. Appl. 2010:383805, 2010), Huang et al. (...
