1. Sharp estimates for generalized k-plane transforms
- Author
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Gressman, Philip T.
- Subjects
- *
RADON transforms , *SUBMANIFOLDS , *MANIFOLDS (Mathematics) , *MATHEMATICAL functions - Abstract
Abstract: In this paper, optimal 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, -improving properties of X-ray like transforms, Math. Res. Lett. 13 (5) (2006) 787–803]) is that full 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 for . [Copyright &y& Elsevier]
- Published
- 2007
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