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

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

, Volume 13 (3) – Oct 28, 2008
22 pages

/lp/springer_journal/boundedness-and-compactness-of-positive-integral-operators-on-cones-of-UB64Fk62mD
Publisher
Birkhäuser-Verlag
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2217-8
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

PositivitySpringer Journals

Published: Oct 28, 2008

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