Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces

By Sanghyuk Lee. 2006

59 citations recorded by the source corpus.

Abstract We obtain bilinear estimates for oscillatory integral operators which are variable coefficient generalizations of bilinear restriction estimates for hypersurfaces. As applications, we improve the known estimates for oscillatory integrals.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b9dfc1e337c619950233671842443f845f00c51c

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Restriction estimates using polynomial partitioning II (2016, methodology): “−1), if p≥ 2· 3n+1 3n−3 for nodd , p≥ 2· 3n+2 3n−2 for neven . RESTRICTION ESTIMATES USING POLYNOMIAL PARTITIONING II 47 Conjecture 11.1 was proven for n= 2 by Hormander in [H] and for n= 3 by Lee in [L] (and a diﬀerent proof was given in [BG]). It is open for n≥ 4. (The best current estimates are g”
Bounds on Oscillatory Integral Operators Based on Multilinear Estimates (2010, background): “St2] kTλfkp≤ ckfk2 for p≥ 2(n+ 1) n− 1 . (1.9) Also, for nodd, there are examples showing that, replacing kfk2 by kfk∞, an inequality (1.8) may only hold for p≥ 2(n+1) n−1 (see [B2]). Lee observed in [L] that Stein’s estimate may be improved if we make the additional hypothesis that Ain (1.7) is pos”
Improved Fourier restriction estimates in higher dimensions (2018, result): “The problem is then to show that the arguments used to study Ef are stable under perturbation; see [21, 6, 13] for recent examples of this approach, producing the current best-known results for the Bochner–Riesz problem.”