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Bak, Jong-Guk; Lee, Jungjin; Lee, Sanghyuk

Bilinear restriction estimates for surfaces of codimension bigger than \(1\). (English) Zbl 1376.42015

Anal. PDE 10, No. 8, 1961-1985 (2017).
Summary: In connection with the restriction problem in \(\mathbb{R}^n\) for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than \(1\). In this paper we show sharp bilinear \(L^2 \times L^2 \rightarrow L^q\) restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates.

Cited in 3 Documents

MSC:

42B15 Multipliers for harmonic analysis in several variables
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Keywords:

Fourier transform of measures; complex surfaces; Fourier restriction estimates
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\textit{J.-G. Bak} et al., Anal. PDE 10, No. 8, 1961--1985 (2017; Zbl 1376.42015)
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