Abstract:

Using the moment inequality for 〖AKρ~D〗mixing
 sequences, 〖AKφ~D〗mixing sequences and truncated method, we investigat
ed the weak convergence, the Lr convergence and the complete convergence f
or weighted sum max〖DD(〗〖〗1≤j≤kn〖DD)〗〖JB((〗∑〖DD(〗j〖〗k
=1〖DD)〗ankXnk-E∑〖DD(〗j〖〗k=1〖DD)〗ankXnk〖JB))〗
 of 〖AKρ~D〗mixing arrays and 〖AKφ~D〗mixing arrays under the
condition of {ank, 1≤k≤kn, n≥1}uniform integrability. The resul
ts presented in this paper have extended and improved some results in related li
terature.

Key words: 〖AKρ~D〗mixing sequence, 〖AKφ~D〗mixing sequence, L^r convergence, complete convergence, {a_nk}uniform integrability