- L q estimates for generalized k - plane transforms Philip
نویسنده
چکیده
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., [9]) is that full Lp − Lq 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 Lp for p < 1.
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