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

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.

### MSC:

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

### References:

 [1] 10.1016/j.jmaa.2013.07.073 · Zbl 1308.42005 [2] 10.1007/s00209-003-0626-8 · Zbl 1073.42006 [3] 10.4310/MRL.2011.v18.n4.a14 · Zbl 1271.42014 [4] 10.4171/RMI/317 · Zbl 1015.42007 [5] 10.1353/ajm.0.0044 · Zbl 1166.42006 [6] 10.1515/crelle-2012-0042 · Zbl 1290.42024 [7] 10.1007/s11511-006-0006-4 · Zbl 1203.42019 [8] 10.1007/978-3-642-66451-9 [9] 10.1007/s00039-011-0140-9 · Zbl 1237.42010 [10] 10.2307/2000407 · Zbl 0563.42010 [11] 10.5565/PUBLMAT_Esco02_05 · Zbl 1024.42006 [12] 10.1090/jams827 · Zbl 1342.42010 [13] 10.1090/S0002-9947-05-03796-7 · Zbl 1092.42003 [14] 10.1215/S0012-7094-99-09617-5 · Zbl 0946.42011 [15] 10.4153/CMB-2005-024-9 · Zbl 1083.42007 [16] ; Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series, 43 (1993) · Zbl 0821.42001 [17] 10.1353/ajm.2016.0021 · Zbl 1341.42022 [18] 10.1007/s00039-003-0449-0 · Zbl 1068.42011 [19] 10.1007/s000390050006 · Zbl 0949.42012 [20] 10.1090/S0894-0347-98-00278-1 · Zbl 0924.42008 [21] 10.1007/s00209-004-0691-7 · Zbl 1071.42009 [22] 10.2307/2661365 · Zbl 1125.42302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.