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 : 12 | Download : 9

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We establish necessary and sufficient conditions on a weight v governing the trace inequality |\hat{K}f|Lqvinsert ignore into journalissuearticles values(\hat{E}); \leq C|f|Lpinsert ignore into journalissuearticles values(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