A bilinear approach to cone multipliers II. Applications

By Terence Tao, Ana Vargas. 2000

155 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/758149ac6ca15f53e8a47152daec245487404fe9

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In Applied Mathematics

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Citations in the corpus

Multilinear weighted convolution of L2 functions, and applications to nonlinear dispersive equations (2000, unknown): “Letd 1,and lets1;s2;s be such that s1 + s2 0; s s1;s2; s< s1 + s2 d 2 or s1 + s2 > 0; s< s1;s2; s s1 + s2 d 2 : Then k k H s(R d ) . k k H s1 (R n ) k k H s2 (R d ) :”
A sharp bilinear restriction estimate for paraboloids (2002, background): “In higher dimensions n ≥ 2, a direct modification of the arguments in [24] gives convergence for s > n/(n+ 3).”
A sharp square function estimate for the cone in ℝ3 (2019, background): “2 of [24].”
Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces (2006, methodology): “1 is essentially sharp and it seems possible to remove the λ -loss for q > (n + 3)/(n + 1) by adapting the argument in [23] which was used to obtain global estimate from local one.”
Littlewood–Paley Decompositions Related to Symmetric Cones and Bergman Projections in Tube Domains (2004, background): “In the ‘blank region’, our main contribution up to now is Theorem 4.25, which gives the equivalence between boundedness of P in L p;q and the inequality kLbfkLp;q . kfkBp;q ; for f 2 D :ð5:1Þ Recall that the natural range of indices for this question is > 12n 1; 16 p <1; 26 q < eq ;p; while the ‘bla”
Sharp L2 estimates of the Schrödinger maximal function in higher dimensions (2018, background): “The higher dimensional case has since been studied by several authors [7, 9, 29, 31, 2, 27, 30, 21, 3, 24, 11, 4, 25, 12, 13].”
Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators (2004, methodology): “Our arguments are similar to those in [9], which make use of the bilinear restriction estimate for the cone (see [24], [14]) with some bilinear techniques developed in [17], [18], and [19] to obtain some sharp L p -”