ON THE OPERATORS OF HARDY-LITTLEWOOD-PÓLYA TYPE

In this paper several new Hardy-Littlewood-Pólya-type operators are introduced and studied. In particular, we study a Hardy-Littlewood-Pólya-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-Pólya-type operators for certain special cases.