  In this paper we introduce and study several new
Hardy-Littlewood-P\'olya-type operators. In particular, we study a
Hardy-Littlewood-P\'olya-type operator induced by a positive Borel measure on
$[0,1)$. We establish some sufficient and necessary conditions for the
boundedness (compactness) of these operators. We also determine the exact
values of the norms of the Hardy-Littlewood-P\'olya-type operators for certain
special cases.
