Boundedness and compactness of positive integral operators on cones of homogeneous groups

摘要

Necessary and sufficient conditions on a weight function v guaranteeing the boundedness/compactness of integral operators with positive kernels defined on cones of homogeneous groups from L p to L v q are established, where $1< p,q < infty$ or $0 < q leq 1< p < infty$ . Behavior of singular numbers for these operators is also studied.