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 V 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.

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M. Vali Siadat is a distinguished professor of mathematics at Richard J. Daley College. He has two doctorates in mathematics, a Ph.D. in pure mathematics and a D.A. in mathematics education. Dr. Siadat has more than thirty publications in mathematics and mathematics education and has had numerous presentations at national mathematics meetings.