Abstract
We extend Hardy's inequality to normalized kernels with the second variable nondecreasing. We also extend the Hardy-Littlewood Maximal theorem to two kinds of kernels, which are nondecreasing, or nonincreasing in the second variable,respectively. As a consequence, the maximal version of Knopp's inequality for integrals are established. Our results give integral versions of Bennett[B2] and Li[L].