Sharp $L^p$-$L^q$ estimates for generalized $k$-plane transforms

Details Sharp $L^p$-$L^q$ estimates for generalized $k$-plane transforms Sharp $L^p$-$L^q$ estimates for generalized $k$-plane transforms

2007-01-04

arxiv.org/abs/math/0701114v1

Mathematics

Classical Analysis and ODEs

23 pages; 1 figure

Scientific paper

In this paper, optimal $L^p-L^q$ estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the $k$-plane transform. An important advance over previous work is that full $L^p-L^q$ estimates are obtained by methods which have traditionally yielded only restricted weak-type estimates. In the process, one is lead to make coercivity estimates for certain functionals on $L^p$ for $p < 1$.

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