A restriction estimate using polynomial partitioning
Abstract
If $S$ is a smooth compact surface in $\mathbb{R}^3$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3.25$, $\| E_S f\|_{L^p(\mathbb{R}^3)} \le C(p,S) \| f \|_{L^\infty(S)}$. The proof uses polynomial partitioning arguments from incidence geometry.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2014
- DOI:
- 10.48550/arXiv.1407.1916
- arXiv:
- arXiv:1407.1916
- Bibcode:
- 2014arXiv1407.1916G
- Keywords:
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- Mathematics - Classical Analysis and ODEs
- E-Print:
- 42 pages. Minor revisions. Accepted for publication in JAMS