Strong laws for weighted sums of random variables satisfying generalized Rosenthal type inequalities

Let 1 < p < 2 and 0 < a,,8 < oo with 1 /p = 1/a + 7,8. 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 EIX1,8 < oo. Let {a k,1 < k < n, n > 1} be an array of constants satisfying Ekn_ ankl a = 0(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. (J. Math. Inequal. 8:465-473, 2014), and Wu et al. (Test 27:379-406, 2018).