Abstract
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 (e.g., [P. Gressman, L p -improving properties of X-ray like transforms, Math. Res. Lett. 13 (5) (2006) 787–803]) 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 led to make coercivity estimates for certain functionals on L p for p < 1 .
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