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

Philip T. Gressman

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

经典分析与常微分方程 2007-05-23 v1

作者: Philip T. Gressman

摘要

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 $p < 1$ .

关键词

operator theory and elliptic operators lp spaces and inequalities special functions and series expansions

引用

@article{arxiv.math/0701114,
  title  = {Sharp $L^p$-$L^q$ estimates for generalized $k$-plane transforms},
  author = {Philip T. Gressman},
  journal= {arXiv preprint arXiv:math/0701114},
  year   = {2007}
}

备注

23 pages; 1 figure

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