A bilinear approach to cone multipliers I. Restriction estimates

By Terence Tao, Ana Vargas. 2000

204 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28739a9b592dad7e997d43627867c18997877993

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators (2004, methodology): “Beyond their results, some specific progress has been made in [1], [2], [17], [18], and [19].”
A sharp bilinear restriction estimate for paraboloids (2002, methodology): “See [22], [23] for more examples of this type of argument.”
Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, background): “There has been significant further progress by Bourgain [17], [19], Wolff [55], Moyua, Vargas, Vega and Tao [38], [50], [49], [48].”
A refinement of the Strichartz inequality for the wave equation with applications (2012, methodology): “Now we use a Whitney decomposition, in the spirit of [57] and [64] (see also [58] and [59]).”
Improved Fourier restriction estimates in higher dimensions (2018, background): “This was proved by Fefferman and Stein in two dimensions [10], but remains open in higher dimensions despite extensive study; see, for example, [1, 2, 6, 8, 9, 11, 12, 23, 27, 32, 34, 35, 36, 37, 38, 39, 43] and the references therein.”
Average decay of the Fourier transform of measures with applications (2015, background): “The higher dimensional case has since been studied by many authors; see for example [17, 12, 33, 39, 6, 30, 37, 36].”
Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds (2018, result): “The results of [46] were improved and extended by a number of authors [27, 17, 18, 6] before the remarkable breakthrough of Bourgain– Demeter [8] established essentially sharp decoupling estimates in all dimensions (see also [5, 43, 24, 30, 28] for alternative approaches to the local smoothing probl”
L p regularity of averages over curves and bounds for associated maximal operators (2005, methodology): “Oberlin, Smith and Sogge [16] used results by Bourgain [3] and Tao and Vargas [21] on square-functions associated to cone multipliers to show that if 2 < p < ∞ then the averages for the helix map Lp to the Sobolev space Lpα, for some α > 2/(3p).”
Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case (2007, result): “Similar arguments can be found in [20], [22], [23].”
Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces (2006, methodology): “We adapt the rescaling argument in [24] (also see [10,22,23,29]).”