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Restriction estimates for certain surfaces of finite type in $\mathbb{R}^3$

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arxiv 2003.00408 v2 pith:MJHBXPPX submitted 2020-03-01 math.AP

classification math.AP
keywords finitetypecertainmathbbrestrictionadaptedargumentsbuschenhenke-m
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abstract

In this paper, we study the restriction estimate for a certain surface of finite type in $\mathbb{R}^3$, and partially improves the results of Buschenhenke-M\"{u}ller-Vargas. The key ingredients of the proof include the so called generalized rescaling technique based on a decomposition adapted to finite type geometry, a decoupling inequality and reduction of dimension arguments.

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