A restriction estimate using polynomial partitioning

Journal of the American Mathematical Society - Tập 29 Số 2 - Trang 371-413
Larry Guth1
1Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Tóm tắt

If S S is a smooth compact surface in R 3 \mathbb {R}^3 with strictly positive second fundamental form, and E S E_S is the corresponding extension operator, then we prove that for all p > 3.25 p > 3.25 , E S f L p ( R 3 ) C ( p , S ) f L ( S ) \| 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.

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