A restriction estimate using polynomial partitioning

2014/07/08 by Guth, Larry · 6 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.1916

Abstract

If S is a smooth compact surface in ℝ³ 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(ℝ³) ≤ C(p,S) ‖ f ‖_L^∞(S). The proof uses polynomial partitioning arguments from incidence geometry.

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