Norm Inequalities for Integral Operators on Cones

In this book we explore the [Lp Lq]-boundedness of certain integral operators on weighted spaces on cones in Rn. These integral operators are of the type ʃV k(x y)f(y)dy defined on a homogeneous cone V. The results of this dissertation are then applied to an important class of operators such as Riemann-Liouville’s fractional integral operators Weyl’s fractional integral operators and Laplace’s operators. As special cases of the above we obtain an Rn-generalization of the celebrated Hardy’s inequality on domains of positivity. We also prove dual results.