Abstract
We extend the Hardy-Littlewood Maximal theorem from the Ces\'aro matrix to the weighted mean matrices with rows increasing and to the N"orlund matrices with rows decreasing. As a consequence, certain generalizations of Hardy's inequality, Knopp's inequality, and Carleman inequality are established. Our results extend the work of Bennett. They are used to estimate the norm of a given matrix. The theory developed here generalizes the corresponding one given in Chang-Pao Chen et al.