- Turkish Journal of Mathematics
- Vol: 38 Issue: 1
- Kernel operators on the upper half-space: boundedness and compactness criteria
Kernel operators on the upper half-space: boundedness and compactness criteria
Authors : Usman Ashraf, Muhammad Asif, Alexander Meskhi
Pages : 119-135
Doi:10.3906/mat-1209-21
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We establish necessary and sufficient conditions on a weight v governing the trace inequality |\hat{K}f|Lqv(\hat{E}) \leq C|f|Lp(E), where E is a cone on a homogeneous group, \hat{E}: = E \times R+ and \hat{K} is a positive kernel operator defined on \hat{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