Article ID Journal Published Year Pages File Type
4668091 Advances in Mathematics 2007 22 Pages PDF
Abstract

In this paper, optimal Lp–Lq estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the k-plane transform. An important advance over previous work (e.g., [P. Gressman, Lp-improving properties of X-ray like transforms, Math. Res. Lett. 13 (5) (2006) 787–803]) is that full Lp–Lq estimates are obtained by methods which have traditionally yielded only restricted weak-type estimates. In the process, one is led to make coercivity estimates for certain functionals on Lp for p<1.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)