On the operators of Hardy-Littlewood-Pólya type

Abstract: 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.