, Volume 13, Issue 3, pp 497–518 | Cite as

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



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.


Operators with positive kernels potentials homogeneous groups trace inequality weights singular numbers of kernel operators 

Mathematics Subject Classification (2000)

Primary 26A33, 42B25 Secondary 43A15, 46B50, 47B10, 47B34 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Abdus Salam School of Mathematical SciencesGC UniversityLahorePakistan
  2. 2.Georgian Academy of SciencesA. Razmadze Mathematical InstituteTbilisiGeorgia

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