Title of article :
Kernel operators on the upper half-space: boundedness and compactness criteria
Author/Authors :
ASHRAF, USMAN COMSATS Institute of Information Technology - Department of Mathematics, Pakistan , ASIF, MUHAMMAD Bahauddin Zakariya University - Centre for Advanced Studies in Pure and Applied Mathematics, Pakistan , MESKHI, ALEXANDER Tbilisi State University - A Razmadze Mathematical Institute of I Javakhishvili, Georgia
Abstract :
We establish necessary and sufficient conditions on a weight v governing the trace inequality ||Kf|| Lq (E) ≤ C ||f|| Lp (E), where E is a cone on a homogeneous group, E:= E ×R+ and K is a positive kernel operator defined on E. Compactness criteria for this operator are also established.
Keywords :
Operators with positive kernels , upper half , space , potentials , homogeneous groups , trace inequality , boundedness , compactness , weights
Journal title :
Turkish Journal of Mathematics
Journal title :
Turkish Journal of Mathematics
