Dergiler / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 1
Kernel operators on the upper half-space: boundedness and compactness criteria
- Sayfa
- 119–135
- DOI
- —
Özet
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.
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.